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# Beginning Algebra LinC Bridg MAT 0024C

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This 11 page Class Notes was uploaded by Gaetano Shields on Thursday October 29, 2015. The Class Notes belongs to MAT 0024C at Valencia College taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/231209/mat-0024c-valencia-college in Mat Mathematics at Valencia College.

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Date Created: 10/29/15

Notes for Week 8 Name MAT 0024C Chapter 9 Roots and Radicals 91 Square Roots and Radical Expressions I Find the principal square root of a given number 39239 The number b is a square root ofthe number a if b2 a Square root notation If a is a positive real number 1 J represents the positive or principal square root of a It is the positive number we square to get a 2 a represents the negative square root of a It is the opposite of the principal square root of a xg 1 3 The principal square root ofO is 0 J6 0 Examples Q Find the square root 64 A Q Find the square root g A Q Find the square root v025 A Approximating Square Roots Use a calculator Example Q Find the square root A Square Roots of Variable Expressions Examples Q Find the square root xz A Q Find the square root ly2 A Find the square root 36x8 gt10 ggto Find the square root 49x64 Applications The Pythagorean Theorem If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse czzb2 02 Examples Q Find the length ofthe missing side x Q Find the length ofthe missing side Q The period T in seconds of a pendulum can be found using the formula T 27139 98 where L represents the length of the pendulum in meters Find the period of a pendulum that is 3528 meters long Give an exact answer and an approximation rounded to the nearest hundredth of a second A 92 Multiplving and Simplifving Square Roots Square Roots of Negative Numbers Square roots 1 If a is a perfect square then J is rational 2 If a is a positive number that is not a perfect square then J is irrational 3 If a is a negative number then J is not a real number Examples Q Classify xE as rational irrational or not a real number A Q Classify V 16 as rational irrational or not a real number A Q Classify 365 as rational irrational or not a real number A The Product Rule for Square Roots The product rule for square roots The square root of the product of two nonnegative numbers is equal to the product of their square roots For any nonnegative real numbers a and b WaZ Examples Q Find the square root xZSJZ A Q Find the square root xIOO A Using the Product Rule to Simplify Square Roots Simpli ed form of a square root 1 Except for 1 the radicand has no perfect square factors 2 No fraction appears in the radicand 3 No radical appears in the denominator of a fraction Simplifying square roots 1 Write the radicand as a product of the greatest perfect square factor and one other factor 2 Use the product rule for square roots to write the expression as a product of square roots 3 Find the square root of the perfect factor Memorize the natural number perfect squares 1 4 916 25 36 49 64 81 100121 144 169 Examples Q Simplify A Q Simplify A Q Simplify A Q Simplify 3x9ysz A Simplify 2s3t52734t7 gt10 93 Dividing and Simplifving Square Roots Dividing Radical Expressions The quotient rule for square roots The quotient of the square roots of two numbers is equal to the square root of the quotient of the two numbers For any positive real numbers a and b b39 Examples E Q Divide and simplify 5 A Q Divide and simplify 18x5 2x3 I A l24xy l27xy3 I Q Divide and simplify A I Rationalizing Denominators Rationalizing monomial denominators To rationalize a square root denominator multiply the numerator and denominator of the given fraction by the square root that appears in its denominator Examples 5 Q Rationalize the denominator A Q Rationalize the denominator 1371 A Q Rationalize the denominator A 94 Adding and Subtracting Sguare Roots Like Radicals 39239 Square root radicals are called like radicals when they have the same radicand Examples Q Are s7x and 7x like radicals A Q Are sSx3 and 8x2 like radicals A Combining Like Radicals Only like radicals can be combined Examples Q Simplify 9 7 A Q Simplify 4amp 75 A Simplify 115w4xy2 715wquotxy2 gt10 Simplifying Radicals in a Sum 01 Difference Examples Q Simplify A Q Simplify A Q Simplify 3 3x125 A Q Simplify 4J56112 A Q Find the perimeter A Q Simplify 27xy3 48xy3 A Multiplying Radical Expressions Examples Q Multiply and simplify B 2 A Q Multiply and simplify 26 J3 A Q Multiply and simplify 1X 4 A Multiply and simplify 3X l20y 6 gt0 Rationalizing Denominators 39239 If a and b are real numbers then a b and a b are called conjugate binomials Rationalizing binomial denominators To rationalize a square root denominator multiply the numerator and denominator of the given fraction by the conjugate of the denominator Q Rationalize the denominator A Q Rationalize the denominator B 5 A

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