 9.1: The graph of a square root function f is shown here. Find each of t...
 9.9.1.1: Fill in the blanks. 5x2 is the _____ root of 25x4 5 because (5x2)2 ...
 9.9.2.1: Fill in the blanks. The expressions 41/2 and (8)2/3 41 have ______ ...
 9.9.3.1: Fill in the blanks.Radical expressions such as 2 4 3 4 and 623 with...
 9.9.7.1: Fill in the blanks. The ____ number i is defined as i 21. We call i...
 9.9.4.1: Fill in the blanks. In this section, we used the ______ rule for ra...
 9.9.6.1: Fill in the blanks. In a right triangle, the side opposite the 90 a...
 9.9.5.1: Fill in the blanks. Equations such as 2x 4 4 5 x and 3 x 1 12 areca...
 9.2: a. Simplify 2100a2. Assume that the variable a is unrestricted. b. ...
 9.9.1.2: Fill in the blanks.The symbol is called a ____ symbol or a ____root...
 9.9.2.2: Fill in the blanks. We read 163/2 as 16 to the three ______ power.
 9.9.3.2: Fill in the blanks. Numbers such as 1, 4, 9, 16, 25, and 36 are cal...
 9.9.7.2: Fill in the blanks. A ______ number is any number that can be writt...
 9.9.4.2: Fill in the blanks. To multiply 2251328 232, use the ______ property.
 9.9.6.2: Fill in the blanks. An _____ right triangle is a right triangle wit...
 9.9.5.2: Fill in the blanks. To solve a radical equation, we find all the va...
 9.3: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.3: Fill in the blanks. A radical symbol represents the ____ or princip...
 9.9.2.3: Fill in the blanks. We read 271/3 as 27 to the onethird power.
 9.9.3.3: Fill in the blanks. The largest perfectsquare _____ of 27 is 9. Th...
 9.9.7.3: Fill in the blanks. For the complex number 2 + 5i, we call 2 the __...
 9.9.4.3: Fill in the blanks. To _____ the denominator of 425, we multiply th...
 9.9.6.3: Fill in the blanks. The _____ theorem states that in a right triang...
 9.9.5.3: Fill in the blanks. When we square both sides of a radical equation...
 9.4: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.4: Fill in the blanks. The number 4 has two square roots, 2 and 2. Whe...
 9.9.2.4: Fill in the blanks. We read (64a5)4/5 as the quantity of 64a5, ____...
 9.9.3.4: Fill in the blanks. To _____ 224 means to write it as 226.
 9.9.7.4: Fill in the blanks. 6 + 3i and 6  3i are called complex ______.
 9.9.4.4: Fill in the blanks. The denominator of the fraction 425 is an _____...
 9.9.6.4: Fill in the blanks. An _____ triangle has three sides of equal leng...
 9.9.5.4: Fill in the blanks. When solving equations containing radicals, fir...
 9.5: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.5: Fill in the blanks. The number 100 has two square roots. The positi...
 9.9.2.5: Fill in the blanks. In the radical expression 24 8 16x8 , 4 is the ...
 9.9.7.5: Fill in the blanks. a. i b. i2 c. i 3 d. i4 e. In general, the powe...
 9.9.3.5: Fill in the blanks. The product rule for radicals: 2n ab. In words,...
 9.9.4.5: Fill in the blanks. To obtain a _____ cube radicand in the denomin...
 9.9.6.5: Fill in the blanks. If and are the lengths of the legs of a right t...
 9.9.5.5: Fill in the blanks. Proposed solutions of a radical equation that d...
 9.6: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.6: Fill in the blanks. In the expression 23 6 27x 6, the _____ is 3 an...
 9.9.2.6: Fill in the blanks. 32 means the fourth _____ of the fifth _____ of...
 9.9.7.6: Fill in the blanks. Simplify: 236 2 36 2 236 6i
 9.9.3.6: Fill in the blanks. The quotient rule for radicals: An ab. In words...
 9.9.4.6: Fill in the blanks. The _____ of is1x 1 1x 1 2 .
 9.9.6.6: Fill in the blanks. In any right triangle, the square of the hypote...
 9.9.5.6: Fill in the blanks. To _____ a proposed solution means to substitut...
 9.7: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.7: Fill in the blanks. When we write 2b4 b22, we say that we have ____...
 9.9.2.7: Complete the table by writing the given expression in the alternate...
 9.9.7.7: Fill in the blanks. a. To add (or subtract) complex numbers, add (o...
 9.9.3.7: Consider the expressions 24 5 and 2425. Which expression is a. the ...
 9.9.4.7: Tell why each of the following expressions is not in simplified rad...
 9.9.6.7: Fill in the blanks. n an isosceles right triangle, the length of th...
 9.9.5.7: Fill in the blanks. a. The power rule for solving radical equations...
 9.8: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.8: Fill in the blanks. When is an odd number, 1n n x represents an ___...
 9.9.2.8: In your own words, explain the three rules for rational exponents i...
 9.9.7.8: Fill in the blanks. To divide 6 7i 1 by 1 8i, we multiply 6 7i1 8i ...
 9.9.3.8: Consider 13 a23 x2 and A3 ax2. Which expression is a. the cube root...
 9.9.4.8: Fill in the blank: To rationalize the denominator of 322, we multip...
 9.9.6.8: Fill in the blanks. The shorter leg of a 30 60 90 triangle is _____...
 9.9.5.8: Determine whether 6 is a solution of each radical equation. a. 2x 3...
 9.9: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.9: Fill in the blanks. (x) 1x x and g(x) 1 are _____ functions.
 9.9.2.9: Graph the following real numbers on a number line. { 82/3, (125)1/3...
 9.9.7.9: Give the complex conjugate of each number. a. 2 3i b. 2 c. 3i
 9.9.3.9: a. Write two radical expressions that have the same radicand but a ...
 9.9.4.9: Fill in the blanks to complete this special product: 5 2x22 ( )2 (5...
 9.9.6.9: Fill in the blanks. The length of the longer leg of a 30 60 90 tria...
 9.9.5.9: What is the first step in solving each equation? a. 2x 11 5 b. 23 5...
 9.10: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.10: Fill in the blanks. Together, 0 and the positive real numbers are c...
 9.9.2.10: a. Evaluate by writing it in the form . b. Evaluate by writing it i...
 9.9.7.10: Factor each numerator. Then remove the factor common to the numerat...
 9.9.3.10: Fill in the blanks. a. 526 326 ( ) 26 26 b. 92 n 7 3 n 223 n (
 9.9.4.10: Fill in the blanks to complete this special product: 1 27 221 27 22...
 9.9.6.10: Fill in the blanks. In a 30 60 90 triangle, the shorter leg is oppo...
 9.9.5.10: Simplify each expression. a. 1 1x 2 b. 1 2x 5 2 c. 23 4x 8 23 d. 1 ...
 9.11: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.11: Fill in the blanks. b is a square root of a if b2 =
 9.9.2.11: Complete each rule for exponents. x 1/n
 9.9.7.11: Complete the illustration. Label the real numbers, the imaginary nu...
 9.9.3.11: Complete each solution. Simplify: 23 32k4 33 4k 33 23 4k 2 3 4k
 9.9.4.11: Perform each operation, if possible. a. 426 226 4 b. 426 1226 2 c. ...
 9.9.6.11: Fill in the blanks. The formula to find the distance between points...
 9.9.5.11: Find: 1 1x 3221
 9.12: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.12: Fill in the blanks. 20 0 and 23 20 0
 9.9.7.12: Determine whether each statement is true or false. a. Every complex...
 9.9.2.12: Complete each rule for exponents. xm/n 1 2n xm x
 9.9.3.12: Complete each solution. Simplify: 280s2t425s2 B80s2t4
 9.9.4.12: Perform each operation, if possible. a. 5 62 62 3 6 b. 51623 c. 302...
 9.9.6.12: Fill in the blanks. Solve for , where represents the length of the ...
 9.9.5.12: Find: 1 25x 2 4221
 9.13: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.13: Fill in the blanks. 24is not a real number, because no real number ...
 9.9.7.13: Complete each solution. (3 2i)(3 i) 3i 2i241. 4 9 3i 3i
 9.9.2.13: Complete each rule for exponents. x m/n m/n 2
 9.9.3.13: Simplify each expression. See Example 1. 250
 9.9.4.13: Fill in the blanks. Multiply: 528 726 5(7)28 352 352 3 351 223 14023
 9.9.6.13: Complete each solution. Evaluate. Approximate to two decimal places...
 9.9.5.13: Complete each solution. Solve: 23x 3 1 59 23x 3 1 23x 3 2 (6) 36 3x...
 9.14: Simplify each expression. Assume that all variables are unrestricte...
 9.9.7.14: Complete each solution. 32 i 32 i 6436 3i35i
 9.9.1.14: Fill in the blanks. 2 3 x y if y3 2 3
 9.9.2.14: Complete each rule for exponents. 1x m/n m/n
 9.9.3.14: Simplify each expression. See Example 1. 228
 9.9.4.14: Fill in the blanks. Rationalize the denominator: 923 4a2 923 4a2 23...
 9.9.6.14: Complete each solution. Solve 8 c 0 2 42 c2 and c 0 assume . Approx...
 9.9.5.14: Fill in the blanks. Write each radical equation using a rational ex...
 9.15: Simplify each expression. Assume that all variables are unrestricte...
 9.9.7.15: Determine whether each statement is true or false. a. 26i i26 b. 28...
 9.9.1.15: Fill in the blanks. 2x 2y and 23 x3 2x 2
 9.9.2.15: Complete each solution. Simplify: 100a4)3/2 1 3 23 1,000a6
 9.9.3.15: Simplify each expression. See Example 1. 8245
 9.9.4.15: Multiply and simplify. All variables represent positive real number...
 9.9.6.15: The lengths of two sides of the right triangle are given. Find the ...
 9.9.5.15: Solve each equation. See Example 1. 2a 3 1 2
 9.16: Simplify each expression. Assume that all variables are unrestricte...
 9.9.7.16: Write each number in the form a + bi. a. 9 11i4b. 1 i18
 9.9.1.16: Fill in the blanks. a. The graph of g(x) 1x 3 is the graph of (x) 1...
 9.9.2.16: Complete each solution. Simplify: (m1/3n1/2)6 1 26(n1/2)6 ( m n6/2 ...
 9.9.3.16: Simplify each expression. See Example 1. 9254
 9.9.4.16: Multiply and simplify. All variables represent positive real number...
 9.9.6.16: The lengths of two sides of the right triangle are given. Find the ...
 9.9.5.16: Solve each equation. See Example 1. 2x 10 1
 9.17: Simplify each expression. Assume that all variables are unrestricte...
 9.9.7.17: Express each number in terms of . See Example 1. 29 2
 9.9.1.17: The graph of a square root function is shown below. Find each of th...
 9.9.2.17: Evaluate each expression. See Example 1. 1251/3
 9.9.3.17: Simplify each expression. See Example 1. 2 40 3 32
 9.9.4.17: Multiply and simplify. All variables represent positive real number...
 9.9.6.17: The lengths of two sides of the right triangle are given. Find the ...
 9.9.5.17: Solve each equation. See Example 1. 24x 5 5 2
 9.18: Simplify each expression. Assume that all variables are unrestricte...
 9.9.7.18: Express each number in terms of . See Example 1. 24
 9.9.1.18: Refer to the graph in problem 17. Estimate each of the following fu...
 9.9.2.18: Evaluate each expression. See Example 1. 81/3
 9.9.3.18: Simplify each expression. See Example 1. 2 2 40
 9.9.4.18: Multiply and simplify. All variables represent positive real number...
 9.9.6.18: The lengths of two sides of the right triangle are given. Find the ...
 9.9.5.18: Solve each equation. See Example 1. 25x 6 2
 9.19: Simplify each expression. Assume that all variables are unrestricte...
 9.9.7.19: Express each number in terms of . See Example 1. 27 2
 9.9.1.19: The graph of a cube root function is shown below. Find each of the ...
 9.9.2.19: Evaluate each expression. See Example 1. 811/4
 9.9.3.19: Simplify each expression. See Example 1. 2 4 48
 9.9.4.19: Multiply and simplify. All variables represent positive real number...
 9.9.6.19: The lengths of two sides of the right triangle are given. Find the ...
 9.9.5.19: Solve each equation. See Example 1. 26x 13 7 2
 9.20: Simplify each expression. Assume that all variables are unrestricte...
 9.9.7.20: Express each number in terms of . See Example 1. 211
 9.9.1.20: Match each function with the correct graph shown below. a. (x) x 1 ...
 9.9.2.20: Evaluate each expression. See Example 1. 6251/4
 9.9.3.20: Simplify each expression. See Example 1. 2 2 32
 9.9.4.20: Multiply and simplify. All variables represent positive real number...
 9.9.6.20: The lengths of two sides of the right triangle are given. Find the ...
 9.9.5.20: Solve each equation. See Example 1. 26x 1 5
 9.21: Simplify each expression. Assume that all variables are unrestricte...
 9.9.7.21: Express each number in terms of . See Example 1. 224 2
 9.9.1.21: Translate each sentence into mathematical symbols. a. The square ro...
 9.9.2.21: Evaluate each expression. See Example 1. 321/5
 9.9.3.21: Simplify each radical expression. All variables represent positive ...
 9.9.4.21: Multiply and simplify. All variables represent positive real number...
 9.9.6.21: The lengths of two sides of the right triangle are given. Find the ...
 9.9.5.21: Solve each equation. See Example 1. B13x 2 8
 9.22: Simplify each expression. Assume that all variables are unrestricte...
 9.9.7.22: Express each number in terms of . See Example 1. 228
 9.9.1.22: Translate each sentence into mathematical symbols. a. f of x equals...
 9.9.2.22: Evaluate each expression. See Example 1. 01/5
 9.9.3.22: Simplify each radical expression. All variables represent positive ...
 9.9.4.22: Multiply and simplify. All variables represent positive real number...
 9.9.6.22: The lengths of two sides of the right triangle are given. Find the ...
 9.9.5.22: Solve each equation. See Example 1. B12x 3 6 B
 9.23: Find the domain of (x) 23x 15.
 9.9.7.23: Express each number in terms of . See Example 1. 272 22
 9.9.1.23: Evaluate each square root without using a calculator. See Objective...
 9.9.2.23: Evaluate each expression. See Example 1. (216)1/3 0
 9.9.3.23: Simplify each radical expression. All variables represent positive ...
 9.9.4.23: Multiply and simplify. All variables represent positive real number...
 9.9.6.23: Find the missing side lengths in each triangle. Give the exact answ...
 9.9.5.23: Solve each equation. Write all proposed solutions. Cross out those ...
 9.24: Geometry. The side of a square with area square feet is given by th...
 9.9.7.24: Express each number in terms of . See Example 1. 224
 9.9.1.24: Evaluate each square root without using a calculator. See Objective...
 9.9.2.24: Evaluate each expression. See Example 1. (1,000)1/3 (
 9.9.3.24: Simplify each radical expression. All variables represent positive ...
 9.9.4.24: Multiply and simplify. All variables represent positive real number...
 9.9.6.24: Find the missing side lengths in each triangle. Give the exact answ...
 9.9.5.24: Solve each equation. Write all proposed solutions. Cross out those ...
 9.25: Cubes. The total surface area of a cube is related to its volume V ...
 9.9.7.25: Express each number in terms of . See Example 1. 5281 62
 9.9.1.25: Evaluate each square root without using a calculator. See Objective...
 9.9.2.25: Evaluate each expression. See Example 1. 161/4
 9.9.3.25: Simplify each radical expression. All variables represent positive ...
 9.9.4.25: Multiply and simplify. All variables represent positive real number...
 9.9.6.25: One leg of an isosceles right triangle is 3.2 feet long. Find the l...
 9.9.5.25: Solve each equation. Write all proposed solutions. Cross out those ...
 9.26: Let g(x) 23 x2 98. Use a calculator fo find g(1.9) to four decimal ...
 9.9.7.26: Express each number in terms of . See Example 1. 6249
 9.9.1.26: Evaluate each square root without using a calculator. See Objective...
 9.9.2.26: Evaluate each expression. See Example 1. 1251/3 16
 9.9.3.26: Simplify each radical expression. All variables represent positive ...
 9.9.4.26: Multiply and simplify. All variables represent positive real number...
 9.9.6.26: One side of a square is 512 in. long. Find the length of its diagon...
 9.9.5.26: Solve each equation. Write all proposed solutions. Cross out those ...
 9.27: Graph each function. Find the domain and range. (x) 1x x
 9.9.7.27: Express each number in terms of . See Example 1. B 259
 9.9.1.27: Evaluate each square root without using a calculator. See Objective...
 9.9.2.27: Evaluate each expression. See Example 1. a14b1/2
 9.9.3.27: Simplify each radical expression. All variables represent positive ...
 9.9.4.27: Multiply and simplify. All variables represent positive real number...
 9.9.6.27: Find the missing side lengths in each triangle. Give the exact answ...
 9.9.5.27: Solve each equation. Write all proposed solutions. Cross out those ...
 9.28: Graph each function. Find the domain and range. (x) 1x
 9.9.7.28: Express each number in terms of . See Example 1. B 121 B 144 2
 9.9.1.28: Evaluate each square root without using a calculator. See Objective...
 9.9.2.28: Evaluate each expression. See Example 1. a 116b1/2
 9.9.3.28: Simplify each radical expression. All variables represent positive ...
 9.9.4.28: Multiply and simplify. All variables represent positive real number...
 9.9.6.28: Find the missing side lengths in each triangle. Give the exact answ...
 9.9.5.28: Solve each equation. Write all proposed solutions. Cross out those ...
 9.29: Graph each function. Find the domain and range. (x) 2x 2 x
 9.9.7.29: Write each number in the form . See Example 2. a. 5 b. 249 2
 9.9.1.29: Evaluate each square root without using a calculator. See Objective...
 9.9.2.29: Simplify each expression. Assume that the variables can be any real...
 9.9.3.29: Simplify each radical expression. All variables represent positive ...
 9.9.4.29: Multiply and simplify. All variables represent positive real number...
 9.9.6.29: Photographs. The diagonal of a square photograph measures 10 inches...
 9.9.5.29: Solve each equation. Write all proposed solutions. Cross out those ...
 9.30: Graph each function. Find the domain and range. (x) 1 x 3
 9.9.7.30: Write each number in the form . See Example 2. a. 43 b. 2169
 9.9.1.30: Evaluate each square root without using a calculator. See Objective...
 9.9.2.30: Simplify each expression. Assume that the variables can be any real...
 9.9.3.30: Simplify each radical expression. All variables represent positive ...
 9.9.4.30: Multiply and simplify. All variables represent positive real number...
 9.9.6.30: Parking Lots. The diagonal of a square parking lot is approximately...
 9.9.5.30: Solve each equation. Write all proposed solutions. Cross out those ...
 9.31: Write each expression in radical form. t1>2
 9.9.7.31: Write each number in the form . See Example 2. a. 225 21 b. 3 28 9
 9.9.1.31: Evaluate each square root without using a calculator. See Objective...
 9.9.2.31: Simplify each expression. Assume that the variables can be any real...
 9.9.3.31: Simplify each radical expression. All variables represent positive ...
 9.9.4.31: Multiply and simplify. All variables represent positive real number...
 9.9.6.31: Find the missing side lengths in each triangle. Give the exact answ...
 9.9.5.31: Solve each equation. Write all proposed solutions. Cross out those ...
 9.32: Write each expression in radical form. (5xy3)1>4
 9.9.7.32: Write each number in the form . See Example 2. a. 21 216 b. 9 212
 9.9.1.32: Evaluate each square root without using a calculator. See Objective...
 9.9.2.32: Simplify each expression. Assume that the variables can be any real...
 9.9.3.32: Simplify each radical expression. All variables represent positive ...
 9.9.4.32: Multiply and simplify. All variables represent positive real number...
 9.9.6.32: Find the missing side lengths in each triangle. Give the exact answ...
 9.9.5.32: Solve each equation. Write all proposed solutions. Cross out those ...
 9.33: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.33: Write each number in the form . See Example 2. a. 76 254 88 b. 7 219 2
 9.9.1.33: Evaluate each square root without using a calculator. See Objective...
 9.9.2.33: Simplify each expression. Assume that the variables can be any real...
 9.9.3.33: Simplify each radical expression. All variables represent positive ...
 9.9.4.33: Multiply and simplify. All variables represent positive real number...
 9.9.6.33: In a 3060 90 triangle, the length of the leg opposite the 30 angle ...
 9.9.5.33: Solve each equation. Write all proposed solutions. Cross out those ...
 9.34: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.34: Write each number in the form . See Example 2. a. 88 298 b. 2 235
 9.9.1.34: Evaluate each square root without using a calculator. See Objective...
 9.9.2.34: Simplify each expression. Assume that the variables can be any real...
 9.9.3.34: Simplify each radical expression. All variables represent positive ...
 9.9.4.34: Multiply and simplify. All variables represent positive real number...
 9.9.6.34: In a 3060 90 triangle, the length of the shorter leg is 522inches. ...
 9.9.5.34: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.5.35: Solve each equation. See Example 5. 3 7n 1 3
 9.35: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.35: Write each number in the form . See Example 2. a. 6 29 45 b. 3 26 8
 9.9.1.35: Use a calculator to find each square root. Give each answer to four...
 9.9.2.35: Simplify each expression. Assume that the variables can be any real...
 9.9.3.35: Simplify each radical expression. All variables represent positive ...
 9.9.4.35: Multiply and simplify. All variables represent positive real number...
 9.9.6.35: Find the missing lengths in each triangle. Give the exact answer an...
 9.9.5.36: Solve each equation. See Example 5. 23 2 12m 4 4 3
 9.36: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.36: Write each number in the form . See Example 2. a. 45 281 b. 8 27
 9.9.1.36: Use a calculator to find each square root. Give each answer to four...
 9.9.2.36: Simplify each expression. Assume that the variables can be any real...
 9.9.3.36: Simplify each radical expression. All variables represent positive ...
 9.9.4.36: Multiply and simplify. All variables represent positive real number...
 9.9.6.36: Find the missing lengths in each triangle. Give the exact answer an...
 9.9.6.37: In a 3060 90 right triangle, the length of the leg opposite the 60 ...
 9.9.5.37: Solve each equation. See Example 5. 2 b 3 x3 7 x 1
 9.37: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.37: Perform the operations. Write all answers in the form a bi. See Exa...
 9.9.1.37: Use a calculator to find each square root. Give each answer to four...
 9.9.2.37: Simplify each expression. Assume that the variables can be any real...
 9.9.3.37: Simplify each radical expression. All variables represent positive ...
 9.9.4.37: Multiply and simplify. All variables represent positive real number...
 9.9.6.38: In a 3060 90 right triangle, the length of the longer leg is yards....
 9.9.5.38: Solve each equation. See Example 5. 23 b3 2 63 b 3 3
 9.38: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.38: Perform the operations. Write all answers in the form a bi. See Exa...
 9.9.1.38: Use a calculator to find each square root. Give each answer to four...
 9.9.2.38: Simplify each expression. Assume that the variables can be any real...
 9.9.3.38: Simplify each radical expression. All variables represent positive ...
 9.9.4.38: Multiply and simplify. All variables represent positive real number...
 9.9.6.39: Find the missing lengths in each triangle. Give the exact answer an...
 9.9.5.39: Solve each equation. See Example 5. (m 3 26)1>3 m 2 73.
 9.39: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.39: Perform the operations. Write all answers in the form a bi. See Exa...
 9.9.1.39: Simplify each expression. Assume that all variables are unrestricte...
 9.9.2.39: Simplify each expression. Assume that the variables can be any real...
 9.9.3.39: Simplify each radical expression. All variables represent positive ...
 9.9.4.39: Multiply and simplify. All variables represent positive real number...
 9.9.6.40: Find the missing lengths in each triangle. Give the exact answer an...
 9.9.5.40: Solve each equation. See Example 5. (x3 56)1>3 ( x 2 3
 9.40: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.40: Perform the operations. Write all answers in the form a bi. See Exa...
 9.9.1.40: Simplify each expression. Assume that all variables are unrestricte...
 9.9.2.40: Simplify each expression. Assume that the variables can be any real...
 9.9.3.40: Simplify each radical expression. All variables represent positive ...
 9.9.4.40: Multiply and simplify. All variables represent positive real number...
 9.9.6.41: In a 30 60 90 right triangle, the length of the hypotenuse is 1.5 f...
 9.9.5.41: Solve each equation. See Example 5. (5r 14) 3 1> 4
 9.41: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.41: Perform the operations. Write all answers in the form a bi. See Exa...
 9.9.1.41: Simplify each expression. Assume that all variables are unrestricte...
 9.9.2.41: Evaluate each expression. See Example 3. 363/2
 9.9.3.41: Simplify each radical expression. All variables represent positive ...
 9.9.4.41: Multiply and simplify. All variables represent positive real number...
 9.9.6.42: In a 30 60 90 right triangle, the length of the hypotenuse is 1223 ...
 9.9.5.42: Solve each equation. See Example 5. (2b 29)1>3 3 1>
 9.42: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.42: Perform the operations. Write all answers in the form a bi. See Exa...
 9.9.1.42: Simplify each expression. Assume that all variables are unrestricte...
 9.9.2.42: Evaluate each expression. See Example 3. 272/3
 9.9.3.42: Simplify each radical expression. All variables represent positive ...
 9.9.4.42: Multiply and simplify. All variables represent positive real number...
 9.9.6.43: Find the exact distance between each pair of points. See Example 7....
 9.9.5.43: See Example 6. Let (x) 4 x 3x 1. For what value(s) of x is (x) 4 ?
 9.43: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.43: Perform the operations. Write all answers in the form a bi. See Exa...
 9.9.1.43: Simplify each expression. Assume that all variables are unrestricte...
 9.9.2.43: Evaluate each expression. See Example 3. 163/4
 9.9.3.43: Simplify each radical expression. All variables represent positive ...
 9.9.4.43: Square or cube each quantity and simplify the result. See Example 4...
 9.9.4.44: Square or cube each quantity and simplify the result. See Example 4...
 9.9.6.44: Find the exact distance between each pair of points. See Example 7....
 9.9.5.44: See Example 6. Let (x) 22x 2 7x . For what value(s) of x is (x) 2 ?
 9.44: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.44: Perform the operations. Write all answers in the form a bi. See Exa...
 9.9.1.44: Simplify each expression. Assume that all variables are unrestricte...
 9.9.2.44: Evaluate each expression. See Example 3. 1003/2 16
 9.9.3.44: Simplify each radical expression. All variables represent positive ...
 9.9.3.45: Simplify each expression. All variables represent positive real num...
 9.9.4.45: Square or cube each quantity and simplify the result. See Example 4...
 9.9.6.45: Find the exact distance between each pair of points. See Example 7....
 9.9.5.45: See Example 6. Let (x) 2 3 3x 6. For what value(s) of x is (x) 3 3?
 9.45: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.45: Multiply. See Example 4. 21 236 29
 9.9.1.45: Simplify each expression. Assume that all variables are unrestricte...
 9.9.2.45: Evaluate each expression. See Example 3. a 1216b2/31
 9.9.2.46: Evaluate each expression. See Example 3. a49b3/2 a
 9.9.3.46: Simplify each expression. All variables represent positive real num...
 9.9.4.46: Square or cube each quantity and simplify the result. See Example 4...
 9.9.6.46: Find the exact distance between each pair of points. See Example 7....
 9.9.5.46: See Example 6. Let (x) 5 4x 4. For what value(s) of x is (x) 2 5?
 9.46: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.46: Multiply. See Example 4. 29 2100
 9.9.1.46: Simplify each expression. Assume that all variables are unrestricte...
 9.9.1.47: Simplify each expression. Assume that all variables are unrestricte...
 9.9.2.47: Evaluate each expression. See Example 3. 45/2 8
 9.9.4.47: Square or cube each quantity and simplify the result. See Example 4...
 9.9.3.47: Simplify each expression. All variables represent positive real num...
 9.9.6.47: Find the exact distance between each pair of points. See Example 7....
 9.9.5.47: Solve each equation. See Example 7. 23x 12 25x 12 2m
 9.47: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.47: Multiply. See Example 4. 22212 23
 9.9.1.48: Simplify each expression. Assume that all variables are unrestricte...
 9.9.4.48: Square or cube each quantity and simplify the result. See Example 4...
 9.9.2.48: Evaluate each expression. See Example 3. (125)4/3 4
 9.9.3.48: Simplify each expression. All variables represent positive real num...
 9.9.6.48: Find the exact distance between each pair of points. See Example 7....
 9.9.5.48: Solve each equation. See Example 7. 2m 4 22m 5
 9.48: Simplify each expression, if possible. Assume that all variables re...
 9.9.7.48: Multiply. See Example 4. 23245
 9.9.4.49: Square or cube each quantity and simplify the result. See Example 4...
 9.9.1.49: Simplify each expression. Assume that all variables are unrestricte...
 9.9.2.49: Simplify each expression. All variables represent positive real num...
 9.9.3.49: Simplify each expression. All variables represent positive real num...
 9.9.6.49: Find the exact distance between each pair of points. See Example 7....
 9.9.5.49: Solve each equation. See Example 7. 224x 1 2x 4 26
 9.49: Perform the operations. Write answers without negative exponents. A...
 9.9.7.49: Multiply. Write all answers in the form . See Example 5. 3(2 9i) 4
 9.9.4.50: Square or cube each quantity and simplify the result. See Example 4...
 9.9.1.50: Simplify each expression. Assume that all variables are unrestricte...
 9.9.3.50: Simplify each expression. All variables represent positive real num...
 9.9.2.50: Simplify each expression. All variables represent positive real num...
 9.9.6.50: Find the exact distance between each pair of points. See Example 7....
 9.9.5.50: Solve each equation. See Example 7. 26 2x 42x 3
 9.50: Perform the operations. Write answers without negative exponents. A...
 9.9.7.50: Multiply. Write all answers in the form . See Example 5. 4(3 4i)
 9.9.4.51: Square or cube each quantity and simplify the result. See Example 4...
 9.9.1.51: Complete each table and then graph the function. Give the domain an...
 9.9.3.51: Simplify each expression. All variables represent positive real num...
 9.9.2.51: Simplify each expression. All variables represent positive real num...
 9.9.6.51: Find the exact distance between each pair of points. See Example 7....
 9.9.5.51: Solve each equation. See Example 7. 26t 9 32t
 9.51: Perform the operations. Write answers without negative exponents. A...
 9.9.7.51: Multiply. Write all answers in the form . See Example 5. 7(5 4i) 5
 9.9.4.52: Square or cube each quantity and simplify the result. See Example 4...
 9.9.3.52: Simplify each expression. All variables represent positive real num...
 9.9.1.52: Complete each table and then graph the function. Give the domain an...
 9.9.2.52: Simplify each expression. All variables represent positive real num...
 9.9.6.52: Find the exact distance between each pair of points. See Example 7....
 9.9.5.52: Solve each equation. See Example 7. 212x 24 61x
 9.52: Perform the operations. Write answers without negative exponents. A...
 9.9.7.52: Multiply. Write all answers in the form . See Example 5. 5(3 2i)
 9.9.4.53: Square or cube each quantity and simplify the result. See Example 4...
 9.9.3.53: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.1.53: Graph each function. Give the domain and range. See Examples 3 and ...
 9.9.2.53: Simplify each expression. All variables represent positive real num...
 9.9.6.53: Find the exact distance between each pair of points. See Example 7....
 9.9.5.53: Solve each equation. See Example 7. (34x 26)1>3 4(x 1)1>3
 9.53: Perform the multiplications. Assume all variables represent positiv...
 9.9.7.53: Multiply. Write all answers in the form . See Example 5. 2i(7 3i) i
 9.9.4.54: Square or cube each quantity and simplify the result. See Example 4...
 9.9.3.54: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.1.54: Graph each function. Give the domain and range. See Examples 3 and ...
 9.9.2.54: Simplify each expression. All variables represent positive real num...
 9.9.6.54: Find the exact distance between each pair of points. See Example 7....
 9.9.5.54: Solve each equation. See Example 7. (a2 2a)1>3 2(a 1)1>3 (3
 9.54: Perform the multiplications. Assume all variables represent positiv...
 9.9.7.54: Multiply. Write all answers in the form . See Example 5. i(8 2i)
 9.9.4.55: Rationalize each denominator. See Example 5. B 27
 9.9.3.55: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.2.55: Simplify each expression. All variables represent positive real num...
 9.9.6.55: Find the midpoint of the line segment with the given endpoints. See...
 9.9.1.55: Find the domain of each function. See Example 4. (x) 2x 6 g
 9.9.5.55: Solve each equation. Write all proposed solutions. Cross out those ...
 9.55: Use rational exponents to simplify each radical. All variables repr...
 9.9.7.55: Multiply. Write all answers in the form . See Example 5. 5i(5 5i) 2i
 9.9.4.56: Rationalize each denominator. See Example 5. 5B 3
 9.9.3.56: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.6.56: Find the midpoint of the line segment with the given endpoints. See...
 9.9.2.56: Simplify each expression. All variables represent positive real num...
 9.9.1.56: Find the domain of each function. See Example 4. g(x) 2x 12
 9.9.5.56: Solve each equation. Write all proposed solutions. Cross out those ...
 9.56: Use rational exponents to simplify each radical. All variables repr...
 9.9.7.56: Multiply. Write all answers in the form . See Example 5. 2i(7 2i)
 9.9.4.57: Rationalize each denominator. See Example 5. B 83
 9.9.3.57: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.6.57: Find the midpoint of the line segment with the given endpoints. See...
 9.9.5.57: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.57: Change each radical to an exponential expression. See Example 5. 2 ...
 9.9.1.57: Find the domain of each function. See Example 4. g(x) 28 2x h(
 9.57: Visibility. The distance in miles a person in an airplane can see t...
 9.9.7.57: Multiply. Write all answers in the form . See Example 6. (2 i)(3 i) (4
 9.9.4.58: Rationalize each denominator. See Example 5. 8B 7
 9.9.3.58: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.6.58: Find the midpoint of the line segment with the given endpoints. See...
 9.9.5.58: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.58: Change each radical to an exponential expression. See Example 5. 27...
 9.9.1.58: Find the domain of each function. See Example 4. h(x) 235 5x
 9.58: Substitute the  and coordinates of each point labeled in the grap...
 9.9.7.58: Multiply. Write all answers in the form . See Example 6. (4 i)(2 i)
 9.9.4.59: Rationalize each denominator. See Example 5. 426
 9.9.3.59: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.6.59: Find the midpoint of the line segment with the given endpoints. See...
 9.9.5.59: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.59: Change each radical to an exponential expression. See Example 5. 23...
 9.9.1.59: Find the domain of each function. See Example 4. s(t) 29t 4 T(
 9.59: Simplify each expression. All variables represent positive real num...
 9.9.7.59: Multiply. Write all answers in the form . See Example 6. (3 2i)(2 3...
 9.9.4.60: Rationalize each denominator. See Example 5. 8210
 9.9.3.60: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.6.60: Find the midpoint of the line segment with the given endpoints. See...
 9.9.5.60: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.60: Change each radical to an exponential expression. See Example 5. 2x...
 9.9.1.60: Find the domain of each function. See Example 4. T(a) 23a 17
 9.60: Simplify each expression. All variables represent positive real num...
 9.9.7.60: Multiply. Write all answers in the form . See Example 6. (3 i)(2 3i)
 9.9.4.61: Rationalize each denominator. See Example 5. 123 2
 9.9.3.61: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.6.61: Find the midpoint of the line segment with the given endpoints. See...
 9.9.5.61: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.61: Change each exponential expression to a radical. See Example 6. (6x...
 9.9.1.61: Find the domain of each function. See Example 4. c(x) 20.5x 20 H(
 9.61: Simplify each expression. All variables represent positive real num...
 9.9.7.61: Multiply. Write all answers in the form . See Example 6. 14 21213 2...
 9.9.4.62: Rationalize each denominator. See Example 5. 223 6
 9.9.3.62: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.6.62: Find the midpoint of the line segment with the given endpoints. See...
 9.9.5.62: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.62: Change each exponential expression to a radical. See Example 6. 7a2...
 9.9.1.62: Find the domain of each function. See Example 4. H(b) 20.4b 36
 9.62: Simplify each expression. All variables represent positive real num...
 9.9.7.62: Multiply. Write all answers in the form . See Example 6. 11 225211 ...
 9.9.4.63: Rationalize each denominator. See Example 5. 323 9
 9.9.3.63: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.6.63: Solve each problem. See Example 9. If (2, 3) is the midpoint of seg...
 9.9.5.63: Solve each equation for the specified variable or expression. See E...
 9.9.2.63: Change each exponential expression to a radical. See Example 6. (2s...
 9.9.1.63: Find each function value, if possible. Do not use a calculator. See...
 9.63: Simplify each expression. All variables represent positive real num...
 9.9.7.63: Multiply. Write all answers in the form . See Example 6. (2 i)2
 9.9.4.64: Rationalize each denominator. See Example 5. 223 a
 9.9.3.64: Simplify by combining like radicals. See Objective 4 and Example 6....
 9.9.6.64: Solve each problem. See Example 9. If (6, 5) is the midpoint of seg...
 9.9.5.64: Solve each equation for the specified variable or expression. See E...
 9.9.2.64: Change each exponential expression to a radical. See Example 6. (x3...
 9.9.1.64: Find each function value, if possible. Do not use a calculator. See...
 9.64: Simplify each expression. All variables represent positive real num...
 9.9.7.64: Multiply. Write all answers in the form . See Example 6. (3 2i)2
 9.9.4.65: Rationalize each denominator. See Example 5. 124 8
 9.9.3.65: Simplify by combining like radicals. All variables represent positi...
 9.9.6.65: Solve each problem. See Example 9. If (7, 3) is the midpoint of QP ...
 9.9.5.65: Solve each equation for the specified variable or expression. See E...
 9.9.2.65: Simplify each expression. All variables represent positive real num...
 9.9.1.65: Find each function value, if possible. Do not use a calculator. See...
 9.65: Simplify each expression. All variables represent positive real num...
 9.9.7.65: Find the product of the given complex number and its conjugate. See...
 9.9.4.66: Rationalize each denominator. See Example 5. 125 2
 9.9.3.66: Simplify by combining like radicals. All variables represent positi...
 9.9.6.66: Solve each problem. See Example 9. If 1 12 , 22 is the midpoint of ...
 9.9.5.66: Solve each equation for the specified variable or expression. See E...
 9.9.2.66: Simplify each expression. All variables represent positive real num...
 9.9.1.66: Find each function value, if possible. Do not use a calculator. See...
 9.66: Simplify each expression. All variables represent positive real num...
 9.9.7.66: Find the product of the given complex number and its conjugate. See...
 9.9.4.67: Rationalize each denominator. All variables represent positive real...
 9.9.3.67: Simplify by combining like radicals. All variables represent positi...
 9.9.6.67: Soccer. The allowable length of a rectangular soccer field used for...
 9.9.5.67: Solve each equation for the specified variable or expression. See E...
 9.9.2.67: Simplify each expression. All variables represent positive real num...
 9.9.1.67: Use a calculator to find each function value. Round to the nearest ...
 9.67: Simplify each expression. All variables represent positive real num...
 9.9.7.67: Find the product of the given complex number and its conjugate. See...
 9.9.4.68: Rationalize each denominator. All variables represent positive real...
 9.9.3.68: Simplify by combining like radicals. All variables represent positi...
 9.9.6.68: Cubes. Find the exact length of the diagonal (in blue) of one of th...
 9.9.5.68: Solve each equation for the specified variable or expression. See E...
 9.9.2.68: Simplify each expression. All variables represent positive real num...
 9.9.1.68: Use a calculator to find each function value. Round to the nearest ...
 9.68: Simplify each expression. All variables represent positive real num...
 9.9.7.68: Find the product of the given complex number and its conjugate. See...
 9.9.4.69: Rationalize each denominator. All variables represent positive real...
 9.9.3.69: Simplify by combining like radicals. All variables represent positi...
 9.9.6.69: Cubes. Find the exact length of the diagonal (in green) of the cube...
 9.9.5.69: Solve each equation for the specified variable or expression. See E...
 9.9.2.69: Simplify each expression. All variables represent positive real num...
 9.9.1.69: Use a calculator to find each function value. Round to the nearest ...
 9.69: Simplify each expression. All variables represent positive real num...
 9.9.7.69: Divide. Write all answers in the form . See Example 8. 95 i
 9.9.4.70: Rationalize each denominator. All variables represent positive real...
 9.9.3.70: Simplify by combining like radicals. All variables represent positi...
 9.9.6.70: Geometry. Use the distance formula to show that a triangle with ver...
 9.9.5.70: Solve each equation for the specified variable or expression. See E...
 9.9.2.70: Simplify each expression. All variables represent positive real num...
 9.9.1.70: Use a calculator to find each function value. Round to the nearest ...
 9.70: Simplify each expression. All variables represent positive real num...
 9.9.7.70: Divide. Write all answers in the form . See Example 8. 42 i
 9.9.4.71: Rationalize each denominator. All variables represent positive real...
 9.9.3.71: Simplify by combining like radicals. All variables represent positi...
 9.9.6.71: Washington, D.C. The square in the map shows the 100 squaremile s...
 9.9.5.71: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.71: Simplify each expression. All variables represent positive real num...
 9.9.1.71: Simplify each cube root. See Example 6. 2 3 1
 9.71: Simplify and combine like radicals. All variables represent positiv...
 9.9.7.71: Divide. Write all answers in the form . See Example 8. 11i4 7i
 9.9.4.72: Rationalize each denominator. All variables represent positive real...
 9.9.3.72: Simplify by combining like radicals. All variables represent positi...
 9.9.6.72: Paper Airplanes. The illustration gives the directions for making a...
 9.9.5.72: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.72: Simplify each expression. All variables represent positive real num...
 9.9.1.72: Simplify each cube root. See Example 6. 23 2 8
 9.72: Simplify and combine like radicals. All variables represent positiv...
 9.9.7.72: Divide. Write all answers in the form . See Example 8. 2i3 8i1
 9.9.4.73: Rationalize each denominator. All variables represent positive real...
 9.9.3.73: Simplify each expression, if possible. All variables represent posi...
 9.9.6.73: Hardware. The sides of a regular hexagonal nut are 10 millimeters l...
 9.9.5.73: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.73: Simplify each expression. All variables represent positive real num...
 9.9.1.73: Simplify each cube root. See Example 6. 2 3 125
 9.73: Simplify and combine like radicals. All variables represent positiv...
 9.9.7.73: Divide. Write all answers in the form . See Example 8. 3 2i4 i2
 9.9.4.74: Rationalize each denominator. All variables represent positive real...
 9.9.3.74: Simplify each expression, if possible. All variables represent posi...
 9.9.6.74: Ironing Boards. Find the height of the ironing board shown in the i...
 9.9.5.74: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.74: Simplify each expression. All variables represent positive real num...
 9.9.1.74: Simplify each cube root. See Example 6. 23 2 27 3
 9.74: Simplify and combine like radicals. All variables represent positiv...
 9.9.7.74: Divide. Write all answers in the form . See Example 8. 6 i2 i3
 9.9.4.75: Rationalize each denominator. All variables represent positive real...
 9.9.3.75: Simplify each expression, if possible. All variables represent posi...
 9.9.6.75: Baseball. A baseball diamond is a square, 90 feet on a side. If the...
 9.9.5.75: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.75: Simplify each cube root. See Example 6. B 3 8 27
 9.9.2.75: Simplify each expression. All variables represent positive real num...
 9.75: Simplify and combine like radicals. All variables represent positiv...
 9.9.7.75: Divide. Write all answers in the form . See Example 8. 7 4i2 5i6
 9.9.4.76: Rationalize each denominator. All variables represent positive real...
 9.9.3.76: Simplify each expression, if possible. All variables represent posi...
 9.9.6.76: Baseball. A shortstop fields a grounder at a point onethird of the...
 9.9.5.76: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.76: Simplify each cube root. See Example 6. B3 125 B 64
 9.9.2.76: Simplify each expression. All variables represent positive real num...
 9.76: Simplify and combine like radicals. All variables represent positiv...
 9.9.7.76: Divide. Write all answers in the form . See Example 8. 2 3i2 3i7
 9.9.4.77: Rationalize each denominator. All variables represent positive real...
 9.9.3.77: Simplify each expression, if possible. All variables represent posi...
 9.9.6.77: Clotheslines. A pair of damp jeans are hung on a clothesline to dry...
 9.9.5.77: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.77: Simplify each cube root. See Example 6. 2 3 64
 9.9.2.77: Simplify each expression. Write the answers without negative expone...
 9.77: Simplify and combine like radicals. All variables represent positiv...
 9.9.7.77: Divide. Write all answers in the form . See Example 8. 7 3i4 2i2
 9.9.4.78: Rationalize each denominator. All variables represent positive real...
 9.9.3.78: Simplify each expression, if possible. All variables represent posi...
 9.9.6.78: Firefighting. The base of the 37foot ladder is 9 feet from the wal...
 9.9.5.78: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.78: Simplify each cube root. See Example 6. 23 2 1,000
 9.9.2.78: Simplify each expression. Write the answers without negative expone...
 9.78: Simplify and combine like radicals. All variables represent positiv...
 9.9.7.78: Divide. Write all answers in the form . See Example 8. 5 3i4 2i7
 9.9.4.79: Rationalize each denominator. All variables represent positive real...
 9.9.3.79: Simplify each expression, if possible. All variables represent posi...
 9.9.6.79: Art History. A figure displaying some of the characteristics of Egy...
 9.9.5.79: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.79: Simplify each cube root. See Example 6. 23 3 216a3 2
 9.9.2.79: Simplify each expression. Write the answers without negative expone...
 9.79: Explain the error in each simplification. a. 225x 325x 5210x b. 30 ...
 9.9.7.79: Divide. Write all answers in the form . See Example 8. 3i3 i5
 9.9.4.80: Rationalize each denominator. All variables represent positive real...
 9.9.3.80: Simplify each expression, if possible. All variables represent posi...
 9.9.6.80: Packaging. The diagonal of a rectangular box with dimensions a x b ...
 9.9.5.80: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.80: Simplify each cube root. See Example 6. 23 512x 23 3 2
 9.80: Sewing. A corner of fabric is folded over to form a collar and stit...
 9.9.2.80: Simplify each expression. Write the answers without negative expone...
 9.9.7.80: Divide. Write all answers in the form . See Example 8. 3 5i1 i1
 9.9.4.81: Rationalize each denominator. All variables represent positive real...
 9.9.3.81: Simplify each expression, if possible. All variables represent posi...
 9.9.6.81: Packaging. An archaeologist wants to ship a 34inch femur bone. Wil...
 9.9.5.81: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.81: Simplify each cube root. See Example 6. 23 3 1,000p6q32
 9.81: Simplify each expression. All variables represent positive real num...
 9.9.2.81: Simplify each expression. Write the answers without negative expone...
 9.9.7.81: Divide. Write all answers in the form . See Example 9. (Hint: Facto...
 9.9.4.82: Rationalize each denominator. All variables represent positive real...
 9.9.3.82: Simplify each expression, if possible. All variables represent posi...
 9.9.6.82: Telephone. The telephone cable in the illustration runs from to to ...
 9.9.5.82: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.82: Simplify each cube root. See Example 6. 23 343a6b 23 3 1,
 9.82: Simplify each expression. All variables represent positive real num...
 9.9.2.82: Simplify each expression. Write the answers without negative expone...
 9.9.7.82: Divide. Write all answers in the form . See Example 9. (Hint: Facto...
 9.9.4.83: Rationalize each denominator. All variables represent positive real...
 9.9.3.83: Simplify each expression, if possible. All variables represent posi...
 9.9.6.83: State the Pythagorean theorem in words.
 9.9.5.83: Solve each equation. Write all proposed solutions. Cross out those ...
 9.83: Simplify each expression. All variables represent positive real num...
 9.9.1.83: Complete each table and then graph the function. Give the domain an...
 9.9.2.83: Simplify each expression. Write the answers without negative expone...
 9.9.7.83: Divide. Write all answers in the form . See Example 9. (Hint: Facto...
 9.9.4.84: Rationalize each denominator. All variables represent positive real...
 9.9.3.84: Simplify each expression, if possible. All variables represent posi...
 9.9.6.84: List the facts that you learned about special right triangles in th...
 9.9.5.84: Solve each equation. Write all proposed solutions. Cross out those ...
 9.84: Simplify each expression. All variables represent positive real num...
 9.9.1.84: Complete each table and then graph the function. Give the domain an...
 9.9.2.84: Simplify each expression. Write the answers without negative expone...
 9.9.7.84: Divide. Write all answers in the form . See Example 9. (Hint: Facto...
 9.9.4.85: Rationalize each denominator. All variables represent positive real...
 9.9.3.85: Simplify each expression, if possible. All variables represent posi...
 9.9.6.85: When the lengths of the sides of a certain triangle are substituted...
 9.9.5.85: Solve each equation. Write all proposed solutions. Cross out those ...
 9.85: Simplify each expression. All variables represent positive real num...
 9.9.1.85: Graph each function. Give the domain and range. See Example 7. (x) ...
 9.9.2.85: Simplify each expression. Write the answers without negative expone...
 9.9.7.85: Divide. Write all answers in the form . See Example 10. 53i
 9.9.4.86: Rationalize each denominator. All variables represent positive real...
 9.9.3.86: Simplify each expression, if possible. All variables represent posi...
 9.9.6.86: Explain how the distance formula and the Pythagorean theorem can be...
 9.9.5.86: Solve each equation. Write all proposed solutions. Cross out those ...
 9.86: Simplify each expression. All variables represent positive real num...
 9.9.1.86: Graph each function. Give the domain and range. See Example 7. (x) ...
 9.9.2.86: Simplify each expression. Write the answers without negative expone...
 9.9.7.86: Divide. Write all answers in the form . See Example 10. 38i
 9.9.4.87: Rationalize each denominator. All variables represent positive real...
 9.9.3.87: Simplify each expression, if possible. All variables represent posi...
 9.9.6.87: Discount Buying. A repairman purchased some washingmachine motors f...
 9.9.5.87: Solve each equation. Write all proposed solutions. Cross out those ...
 9.87: Simplify each expression. All variables represent positive real num...
 9.9.1.87: Evaluate each radical expression, if possible, without using a calc...
 9.9.2.87: Simplify each expression. Write the answers without negative expone...
 9.9.7.87: Divide. Write all answers in the form . See Example 10. 27i
 9.9.4.88: Rationalize each denominator. All variables represent positive real...
 9.9.3.88: Simplify each expression, if possible. All variables represent posi...
 9.9.6.88: Aviation. An airplane can fly 650 miles with the wind in the same a...
 9.9.5.88: Solve each equation. Write all proposed solutions. Cross out those ...
 9.88: Simplify each expression. All variables represent positive real num...
 9.9.1.88: Evaluate each radical expression, if possible, without using a calc...
 9.9.2.88: Simplify each expression. Write the answers without negative expone...
 9.9.7.88: Divide. Write all answers in the form . See Example 10. 85i
 9.9.4.89: Rationalize each denominator. All variables represent positive real...
 9.9.3.89: Simplify each expression, if possible. All variables represent posi...
 9.9.6.89: Find the length of the diagonal of the cube shown in figure (a) below.
 9.9.5.89: Solve each equation. Write all proposed solutions. Cross out those ...
 9.89: Simplify each expression. All variables represent positive real num...
 9.9.1.89: Evaluate each radical expression, if possible, without using a calc...
 9.9.2.89: Perform the multiplications. All variables represent positive real ...
 9.9.7.89: Simplify each expression. See Example 11. i21
 9.9.7.90: Simplify each expression. See Example 11. i19
 9.9.4.90: Rationalize each denominator. All variables represent positive real...
 9.9.3.90: Simplify each expression, if possible. All variables represent posi...
 9.9.6.90: Show that the length of the diagonal of the rectangular solid shown...
 9.9.5.90: Solve each equation. Write all proposed solutions. Cross out those ...
 9.90: Simplify each expression. All variables represent positive real num...
 9.9.1.90: Evaluate each radical expression, if possible, without using a calc...
 9.9.2.90: Perform the multiplications. All variables represent positive real ...
 9.9.7.91: Simplify each expression. See Example 11. i27
 9.9.4.91: Rationalize each denominator. All variables represent positive real...
 9.9.3.91: Simplify each expression, if possible. All variables represent posi...
 9.9.6.91: Find the distance between each pair of points. 1 248, 2150 2 and 1 ...
 9.9.5.91: Solve each equation. Write all proposed solutions. Cross out those ...
 9.91: Simplify each expression. All variables represent positive real num...
 9.9.1.91: Evaluate each radical expression, if possible, without using a calc...
 9.9.2.91: Perform the multiplications. All variables represent positive real ...
 9.9.7.92: Simplify each expression. See Example 11. i22
 9.9.4.92: Rationalize each denominator. All variables represent positive real...
 9.9.3.92: Simplify each expression, if possible. All variables represent posi...
 9.9.6.92: Find the distance between each pair of points. 1 28, 220 2 and 1 25...
 9.9.5.92: Solve each equation. Write all proposed solutions. Cross out those ...
 9.92: Simplify each expression. All variables represent positive real num...
 9.9.1.92: Evaluate each radical expression, if possible, without using a calc...
 9.9.2.92: Perform the multiplications. All variables represent positive real ...
 9.9.7.93: Simplify each expression. See Example 11. i100
 9.9.4.93: Rationalize each denominator. All variables represent positive real...
 9.9.3.93: Simplify each expression, if possible. All variables represent posi...
 9.9.5.93: Solve each equation. Write all proposed solutions. Cross out those ...
 9.93: Rationalize each denominator. All variables represent positive real...
 9.9.1.93: Evaluate each radical expression, if possible, without using a calc...
 9.9.2.93: Use rational exponents to simplify each radical. All variables repr...
 9.9.7.94: Simplify each expression. See Example 11. i97
 9.9.4.94: Rationalize each denominator. All variables represent positive real...
 9.9.3.94: Simplify each expression, if possible. All variables represent posi...
 9.9.5.94: Solve each equation. Write all proposed solutions. Cross out those ...
 9.94: Rationalize each denominator. All variables represent positive real...
 9.9.2.94: Use rational exponents to simplify each radical. All variables repr...
 9.9.1.94: Evaluate each radical expression, if possible, without using a calc...
 9.9.7.95: Simplify each expression. See Example 11. i42
 9.9.4.95: Rationalize each denominator. All variables represent positive real...
 9.9.3.95: Simplify each expression, if possible. All variables represent posi...
 9.9.5.95: Solve each equation. Write all proposed solutions. Cross out those ...
 9.95: Rationalize each denominator. All variables represent positive real...
 9.9.2.95: Use rational exponents to simplify each radical. All variables repr...
 9.9.1.95: Simplify each radical expression. Assume all variables are unrestri...
 9.9.7.96: Simplify each expression. See Example 11. i200
 9.9.4.96: Rationalize each denominator. All variables represent positive real...
 9.9.3.96: Simplify each expression, if possible. All variables represent posi...
 9.9.5.96: Solve each equation. Write all proposed solutions. Cross out those ...
 9.96: Rationalize each denominator. All variables represent positive real...
 9.9.2.96: Use rational exponents to simplify each radical. All variables repr...
 9.9.1.96: Simplify each radical expression. Assume all variables are unrestri...
 9.9.7.97: Perform the operations. Write all answers in the form a + bi. (3 i)...
 9.9.4.97: Rationalize each denominator. All variables represent positive real...
 9.9.3.97: Simplify each expression, if possible. All variables represent posi...
 9.9.5.97: Solve each equation. Write all proposed solutions. Cross out those ...
 9.97: Rationalize each denominator. All variables represent positive real...
 9.9.2.97: Use rational exponents to simplify each radical. All variables repr...
 9.9.1.97: Simplify each radical expression. Assume all variables are unrestri...
 9.9.7.98: Perform the operations. Write all answers in the form a + bi. (14 4...
 9.9.4.98: Rationalize each denominator. All variables represent positive real...
 9.9.3.98: Simplify each expression, if possible. All variables represent posi...
 9.9.5.98: Solve each equation. Write all proposed solutions. Cross out those ...
 9.98: Rationalize each denominator. All variables represent positive real...
 9.9.2.98: Use rational exponents to simplify each radical. All variables repr...
 9.9.1.98: Simplify each radical expression. Assume all variables are unrestri...
 9.9.7.99: Perform the operations. Write all answers in the form a + bi. 12 21...
 9.9.4.99: Rationalize each numerator. All variables represent positive real n...
 9.9.3.99: Simplify each expression, if possible. All variables represent posi...
 9.9.5.99: Solve each equation. Write all proposed solutions. Cross out those ...
 9.99: Rationalize the numerator: 1a 2b1a
 9.9.2.99: Use rational exponents to simplify each radical. All variables repr...
 9.9.1.99: Simplify each radical expression. Assume all variables are unrestri...
 9.9.7.100: Perform the operations. Write all answers in the form a + bi. (3 24...
 9.9.4.100: Rationalize each numerator. All variables represent positive real n...
 9.9.3.100: Simplify each expression, if possible. All variables represent posi...
 9.9.5.100: Solve each equation. Write all proposed solutions. Cross out those ...
 9.100: Volume. The formula relating the radius of a sphere and its volume ...
 9.9.2.100: Use rational exponents to simplify each radical. All variables repr...
 9.9.1.100: Simplify each radical expression. Assume all variables are unrestri...
 9.9.7.101: Perform the operations. Write all answers in the form a + bi. (6 9i...
 9.9.4.101: Rationalize each numerator. All variables represent positive real n...
 9.9.3.101: Simplify each expression, if possible. All variables represent posi...
 9.9.5.101: Solve each equation. Write all proposed solutions. Cross out those ...
 9.101: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.101: Use rational exponents to simplify each radical. All variables repr...
 9.9.1.101: Simplify each radical expression. Assume all variables are unrestri...
 9.9.7.102: Perform the operations. Write all answers in the form a + bi. (3 11...
 9.9.4.102: Rationalize each numerator. All variables represent positive real n...
 9.9.3.102: Simplify each expression, if possible. All variables represent posi...
 9.9.5.102: Solve each equation. Write all proposed solutions. Cross out those ...
 9.102: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.102: Use rational exponents to simplify each radical. All variables repr...
 9.9.1.102: Simplify each radical expression. Assume all variables are unrestri...
 9.9.7.103: Perform the operations. Write all answers in the form a + bi. 2i3 2i
 9.9.4.103: The following problems involve addition, subtraction, and multiplic...
 9.9.3.103: Simplify each expression, if possible. All variables represent posi...
 9.9.5.103: Solve each equation. Write all proposed solutions. Cross out those ...
 9.103: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.103: Use rational exponents to simplify each radical. All variables repr...
 9.9.1.103: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.104: Perform the operations. Write all answers in the form a + bi. 4i2 6i2
 9.9.4.104: The following problems involve addition, subtraction, and multiplic...
 9.9.3.104: Simplify each expression, if possible. All variables represent posi...
 9.9.5.104: Solve each equation. Write all proposed solutions. Cross out those ...
 9.104: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.104: Simplify each radical expression, if possible. Assume all variables...
 9.9.2.104: Use rational exponents to simplify each radical. All variables repr...
 9.9.7.105: Perform the operations. Write all answers in the form a + bi. 6i(2 ...
 9.9.4.105: The following problems involve addition, subtraction, and multiplic...
 9.9.3.105: Simplify each expression, if possible. All variables represent posi...
 9.9.5.105: Highway Design. A curved road will accommodate traffic traveling mp...
 9.105: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.105: Simplify each radical expression, if possible. Assume all variables...
 9.9.2.105: Use a calculator to evaluate each expression. Round to the nearest ...
 9.9.7.106: Perform the operations. Write all answers in the form a + bi. 9i(4 ...
 9.9.4.106: The following problems involve addition, subtraction, and multiplic...
 9.9.3.106: Simplify each expression, if possible. All variables represent posi...
 9.9.5.106: Forestry. The taller a lookout tower, the farther an observer can s...
 9.106: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.106: Simplify each radical expression, if possible. Assume all variables...
 9.9.2.106: Use a calculator to evaluate each expression. Round to the nearest ...
 9.9.7.107: Perform the operations. Write all answers in the form a + bi. 45i35
 9.9.4.107: The following problems involve addition, subtraction, and multiplic...
 9.9.3.107: Simplify each expression, if possible. All variables represent posi...
 9.9.5.107: Wind Power. The power generated by a windmill is related to the vel...
 9.107: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.107: Simplify each radical expression, if possible. Assume all variables...
 9.9.2.107: Use a calculator to evaluate each expression. Round to the nearest ...
 9.9.7.108: Perform the operations. Write all answers in the form a + bi. 32i17
 9.9.4.108: The following problems involve addition, subtraction, and multiplic...
 9.9.3.108: Simplify each expression, if possible. All variables represent posi...
 9.9.5.108: Diamonds. The effective rate of interest earned by an investment is...
 9.108: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.1.108: Simplify each radical expression, if possible. Assume all variables...
 9.9.2.108: Use a calculator to evaluate each expression. Round to the nearest ...
 9.9.7.109: Perform the operations. Write all answers in the form a + bi. 12 i2...
 9.9.4.109: The following problems involve addition, subtraction, and multiplic...
 9.9.3.109: Simplify each expression, if possible. All variables represent posi...
 9.9.5.109: General Contractor During construction, carpenters often brace wall...
 9.109: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.109: Simplify each expression. All variables represent positive real num...
 9.9.1.109: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.110: Perform the operations. Write all answers in the form a + bi. 15 i2...
 9.9.4.110: The following problems involve addition, subtraction, and multiplic...
 9.9.3.110: Simplify each expression, if possible. All variables represent posi...
 9.9.5.110: Theater Productions. The ropes, pulleys, and sandbags shown in the ...
 9.110: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.110: Simplify each expression. All variables represent positive real num...
 9.9.1.110: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.111: Perform the operations. Write all answers in the form a + bi. 5 9i1 i1
 9.9.4.111: The following problems involve addition, subtraction, and multiplic...
 9.9.3.111: Simplify each expression, if possible. All variables represent posi...
 9.9.5.111: Supply and Demand. The number of wrenches that will be produced at ...
 9.111: Let (x) 25x 1 g and g(x) x 1. For what values of x is(x) g(x)?
 9.9.2.111: Simplify each expression. All variables represent positive real num...
 9.9.1.111: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.112: Perform the operations. Write all answers in the form a + bi. 5 i3 2i5
 9.9.4.112: The following problems involve addition, subtraction, and multiplic...
 9.9.3.112: Simplify each expression, if possible. All variables represent posi...
 9.9.5.112: Supply and Demand. The number of mirrors that will be produced at a...
 9.112: Let (x) 22x x 2 7x. For what value(s) of x is (x) 2?
 9.9.2.112: Simplify each expression. All variables represent positive real num...
 9.9.1.112: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.113: Perform the operations. Write all answers in the form a + bi. (4 8i)2
 9.9.4.113: The following problems involve addition, subtraction, and multiplic...
 9.9.3.113: First give the exact answer, expressed as a simplified radical expr...
 9.9.5.113: What is wrong with the work shown below? Solve: x 10x 1 111 23 x 1 ...
 9.113: Solve each equation for the specified variable. r P BAfor P
 9.9.2.113: Simplify each expression. All variables represent positive real num...
 9.9.1.113: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.114: Perform the operations. Write all answers in the form a + bi. (7 3i)2
 9.9.4.114: The following problems involve addition, subtraction, and multiplic...
 9.9.3.114: First give the exact answer, expressed as a simplified radical expr...
 9.9.5.114: The first step of a students solution is shown below. What is a bet...
 9.114: Solve each equation for the specified variable. h for I B 3 12I b f...
 9.9.2.114: Simplify each expression. All variables represent positive real num...
 9.9.1.114: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.115: Perform the operations. Write all answers in the form a + bi. 25 i2...
 9.9.4.115: The following problems involve addition, subtraction, and multiplic...
 9.9.3.115: First give the exact answer, expressed as a simplified radical expr...
 9.9.5.115: Explain the error in the following work. Solve: 22y 1 2y 7 31 22y 1...
 9.115: Carpentry. The gable end of the roof shown below is divided in half...
 9.9.2.115: Simplify each expression. All variables represent positive real num...
 9.9.1.115: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.116: Perform the operations. Write all answers in the form a + bi. 23 i2...
 9.9.4.116: The following problems involve addition, subtraction, and multiplic...
 9.9.3.116: First give the exact answer, expressed as a simplified radical expr...
 9.9.5.116: Explain why it is immediately apparent that 28x 7 2 has no solution.
 9.116: Sailing. A technique called tacking allows a sailboat to make progr...
 9.9.2.116: Simplify each expression. All variables represent positive real num...
 9.9.1.116: Simplify each radical expression, if possible. Assume all variables...
 9.9.1.117: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.117: Perform the operations. Write all answers in the form a + bi. a. 28...
 9.9.4.117: The following problems involve addition, subtraction, and multiplic...
 9.9.3.117: First give the exact answer, expressed as a simplified radical expr...
 9.9.5.117: To solve the equation 22x 7 1x we need only square both sides once....
 9.117: For problems 117122, give the exact answer and then an approximatio...
 9.9.2.117: Simplify each expression. All variables represent positive real num...
 9.9.1.118: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.118: Perform the operations. Write all answers in the form a + bi. a. (3...
 9.9.4.118: The following problems involve addition, subtraction, and multiplic...
 9.9.3.118: First give the exact answer, expressed as a simplified radical expr...
 9.9.5.118: Explain how to solve 2x 2 2 4 using the graphs below. f(x) = x 2 + ...
 9.118: For problems 117122, give the exact answer and then an approximatio...
 9.9.2.118: Simplify each expression. All variables represent positive real num...
 9.9.1.119: Simplify each radical expression, if possible. Assume allvariables ...
 9.9.7.119: Perform the operations. Write all answers in the form a + bi. a. (2...
 9.9.4.119: The following problems involve addition, subtraction, and multiplic...
 9.9.3.119: Explain why each expression is not in simplified form. a. 23 9x4 b....
 9.119: For problems 117122, give the exact answer and then an approximatio...
 9.9.5.119: Explain how the table can be used to solve 24x 3 2 22x 5 if Y1 24x ...
 9.9.2.119: Simplify each expression. All variables represent positive real num...
 9.9.1.120: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.120: Perform the operations. Write all answers in the form a + bi. a. 29...
 9.9.4.120: The following problems involve addition, subtraction, and multiplic...
 9.9.3.120: How are the procedures used to simplify 3x 4x and 32x 42x similar?
 9.120: For problems 117122, give the exact answer and then an approximatio...
 9.9.5.120: Explain how to use the graph of (x) 23 x 0.5 1Y2, shown in the illu...
 9.9.2.120: Simplify each expression. All variables represent positive real num...
 9.9.1.121: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.121: Fractals. Complex numbers are fundamental in the creation of the in...
 9.9.4.121: The following problems involve addition, subtraction, and multiplic...
 9.9.3.121: Explain the mistake in the students solution shown below. Simplify:...
 9.121: Find x and y. x y5454590
 9.9.5.121: Lighting. The intensity of light from a lightbulb varies inversely ...
 9.9.2.121: Simplify each expression. All variables represent positive real num...
 9.9.2.122: Simplify each expression. All variables represent positive real num...
 9.9.1.122: Simplify each radical expression, if possible. Assume all variables...
 9.9.7.122: Electronics. The impedance in an AC (alternating current) circuit i...
 9.9.4.122: The following problems involve addition, subtraction, and multiplic...
 9.9.3.122: Explain how the graphs of Y1 3224x 254x (on the left) and Y1 926x (...
 9.122: Find x and y. 50xy90 3060
 9.9.5.122: Property Tax. The property tax in a certain county varies directly ...
 9.9.2.123: Simplify each expression. All variables represent positive real num...
 9.9.1.123: Use a calculator to solve each problem. Round answers to the neares...
 9.9.7.123: What is an imaginary number? What is a complex number?
 9.9.4.123: The following problems involve addition, subtraction, and multiplic...
 9.9.3.123: Perform each operation. 3x2y3(5x3y4)[5
 9.123: Find the distance between the points. (1, 3) and (6, 9)
 9.9.5.123: Typesetting. If 12point type is 0.166044 inch tall, how tall is 30...
 9.9.2.124: Simplify each expression. All variables represent positive real num...
 9.9.1.124: Pendulums. Find the period of a pendulum with length 1 foot. See Ex...
 9.9.7.124: The method used to divide complex numbers is similar to the method ...
 9.9.4.124: The following problems involve addition, subtraction, and multiplic...
 9.9.3.124: Perform each operation. (2x2 9x 5) x2x2 x 3x
 9.124: Find the distance between the points. (4, 6) and (2, 8)
 9.9.5.124: Guitar Strings. The frequency of vibration of a string varies direc...
 9.9.2.125: Simplify each expression. All variables represent positive real num...
 9.9.1.125: Shoelaces. The formula S 2CH L (p 1)2H2 V2DV can be used to calcula...
 9.9.7.125: Explain the error. Then find the correct result. a. Add: 216 29 225...
 9.9.4.125: The following problems involve addition, subtraction, andmultiplica...
 9.9.3.125: Perform each operation. 2p 56p2 7p 25(2
 9.125: Find the midpoint of the segment joining (8, 2) and (6, 4).
 9.9.5.125: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.126: Simplify each expression. All variables represent positive real num...
 9.9.1.126: Baseball. The length of a diagonal of a square is given by the func...
 9.9.7.126: Determine whether the pair of complex numbers are equal. Explain yo...
 9.9.4.126: The following problems involve addition, subtraction, andmultiplica...
 9.9.3.126: Perform each operation. xy1x 1y
 9.126: If (6, 1) is the midpoint of segment PQ and the coordinates of P ar...
 9.9.5.126: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.127: Simplify each expression. All variables represent positive real num...
 9.9.7.127: Wind Speeds. A plane that can fly 200 mph in still air makes a 330...
 9.9.1.127: Pulse Rates. The approximate pulse rate (in beats per minute) of an...
 9.9.4.127: The following problems involve addition, subtraction, andmultiplica...
 9.9.3.127: Simplify each expression. All variables represent positive real num...
 9.127: Write each expression in terms of i. 225 2
 9.9.5.127: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.128: Simplify each expression. All variables represent positive real num...
 9.9.7.128: Finding Rates. A student drove a distance of 135 miles at an averag...
 9.9.1.128: The Grand Canyon. The time (in seconds) that it takes for an object...
 9.9.4.128: The following problems involve addition, subtraction, andmultiplica...
 9.9.3.128: Simplify each expression. All variables represent positive real num...
 9.128: Write each expression in terms of i. 218
 9.9.5.128: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.129: Simplify each expression. All variables represent positive real num...
 9.9.7.129: Simplify: ( i349) i456
 9.9.1.129: Biology. Scientists will place five rats inside a clear plastic hem...
 9.9.4.129: Statistics. An example of a normal distribution curve, or bellshap...
 9.9.3.129: Simplify each expression. All variables represent positive real num...
 9.129: Write each expression in terms of i. 26
 9.9.5.129: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.130: Simplify each expression. All variables represent positive real num...
 9.9.7.130: Simplify (2 3i)2i and write the result in the form a + bi.
 9.9.1.130: Aquariums. The function s(g) 33 g7.5 determines how long (in feet) ...
 9.9.4.130: Analytical Geometry. The length of the perpendicular segment drawn ...
 9.9.3.130: Simplify each expression. All variables represent positive real num...
 9.130: Write each expression in terms of i. B 964 2
 9.9.5.130: Solve each equation. Write all proposed solutions. Cross out those ...
 9.9.2.131: Simplify each expression. All variables represent positive real num...
 9.9.1.131: Collectibles. The effective rate of interest r earned by an investm...
 9.9.4.131: Trigonometry. In trigonometry, we often must find the ratio of the ...
 9.9.3.131: Simplify each expression. All variables represent positive real num...
 9.131: Complete the diagram. Complex numbersnumbers numbers
 9.9.2.132: Simplify each expression. All variables represent positive real num...
 9.9.1.132: Law Enforcement. The graphs of the two radical functions shown in t...
 9.9.4.132: Engineering. Refer to the illustration below that shows a block con...
 9.9.3.132: Simplify each expression. All variables represent positive real num...
 9.132: Determine whether each statement is true or false. a. Every real nu...
 9.9.2.133: Simplify each expression. All variables represent positivereal numb...
 9.9.1.133: If is any real number, that is, if is unrestricted, then 2x2 xis no...
 9.9.4.133: Consider 2327 2327 2727. Explain why the expressions on the left si...
 9.133: Give the complex conjugate of each number. a. 3 6i b. 19i
 9.9.2.134: Simplify each expression. All variables represent positivereal numb...
 9.9.1.134: Explain why 236 is just 6, and not also 6 .
 9.9.4.134: To rationalize the denominator of 2412243, why wouldnt we multiply ...
 9.134: Give the complex conjugate of each number. a. 1 7i b. i
 9.9.2.135: Simplify each expression. All variables represent positivereal numb...
 9.9.1.135: Explain what is wrong with the graph in the illustration if it is s...
 9.9.4.135: Explain why 2312235is not in simplified form.
 9.135: Perform the operations. Write all answers in the form a + bi. (3 4i...
 9.9.2.136: Simplify each expression. All variables represent positivereal numb...
 9.9.1.136: Explain how to estimate the domain and range of the radical functio...
 9.9.4.136: Explain why 3 3a11kis not in simplified form.
 9.136: Perform the operations. Write all answers in the form a + bi. 17 29...
 9.9.2.137: Ballistic Pendulums. The formula v m Mm (2gh)1/2 gives the velocity...
 9.9.1.137: Perform the operations and simplify when possible. x2 3xy 4y2x2 cx ...
 9.9.4.137: Explain why 2m 2m m m but 23 m 23 2m 2m m m m. Assume that m repres...
 9.137: Perform the operations. Write all answers in the form a + bi. 3i(2 ...
 9.9.2.138: Geography. The formula A [s(s a)(s b)(s c)]1/2m = gives the area of...
 9.9.1.138: Perform the operations and simplify when possible. 2x 33x 1 x 42x 1x
 9.9.4.138: Explain why the product of 2m 3 2 and 2m 3 does not contain a radical.
 9.138: Perform the operations. Write all answers in the form a + bi. 2 7i)...
 9.9.2.139: Relativity. One concept of relativity theory is that an object movi...
 9.9.1.139: Graph (x) 2x 2 32x and find the domain and range.
 9.9.4.139: Solve each equation. 8b 232 b 1b2m
 9.139: Perform the operations. Write all answers in the form a + bi. 2 2 3 29
 9.9.2.140: Logging. The width and height of the strongest rectangular beam tha...
 9.9.1.140: Simplify 29a a 0 16 12a8b25 4b50and assume that and . b 0 29a a 0 1
 9.140: Perform the operations. Write all answers in the form a + bi. (9i) 2 2
 9.9.4.140: Solve each equation. 2x 21x 1 1(x 1)(x 2)8b
 9.9.2.141: General Contractor The length of the longest board that can be carr...
 9.141: Perform the operations. Write all answers in the form a + bi. 5 14i...
 9.9.4.141: Multiply: 22 23 2. (Hint: Keep in mind two things. The indices (plu...
 9.9.2.142: Cubicles. The area of the base of a cube is given by the function A...
 9.142: Perform the operations. Write all answers in the form a + bi. 311i
 9.9.4.142: Show that 23 a2 13 a23 b 23 b223 a2 13 a23 b 23 b222 can be used to...
 9.9.2.143: What is a rational exponent? Give some examples.
 9.143: Simplify each expression. i42
 9.9.2.144: Explain how the root key 1x yon a scientific calculator can be used...
 9.144: Simplify each expression. i97
 9.9.2.145: Commuting Time. The time it takes a car to travel a certain distanc...
 9.9.2.146: Bankruptcy. After filing for bankruptcy, a company was able to pay ...
 9.9.2.147: The fraction 24 is equal to1 2/42 . Is equal to 161/2 ? Explain.
 9.9.2.148: Explain how would you evaluate an expression with a mixednumber ex...
Solutions for Chapter 9: Radical Expressions and Equations
Full solutions for Elementary and Intermediate Algebra  5th Edition
ISBN: 9781111567682
Solutions for Chapter 9: Radical Expressions and Equations
Get Full SolutionsSince 1058 problems in chapter 9: Radical Expressions and Equations have been answered, more than 37103 students have viewed full stepbystep solutions from this chapter. Chapter 9: Radical Expressions and Equations includes 1058 full stepbystep solutions. This textbook survival guide was created for the textbook: Elementary and Intermediate Algebra, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Elementary and Intermediate Algebra was written by and is associated to the ISBN: 9781111567682.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.