 75.1: 5 63
 75.2: 16 x 5 y 4 3
 75.3: 75 x 3 y 6 4.
 75.4: _7 8y
 75.5: a 7 _ b 9 6
 75.6: 3 _2 3x
 75.7: Write the formula without a radical in the denominator.
 75.8: How fast was a car traveling that left skid marks 120 feet long?
 75.9: (2 15 )(4 21 ) 10
 75.10: 2a b 2 6 a 3 b 2 11.
 75.11: 3 _ 625 3 25 12.
 75.12: 3  2 4 3 + 4 3 + 5 4 3 13. 3
 75.13: 3 3 128 + 5 3 16 14.
 75.14: (3  5 )(1 + 3 ) 15
 75.15: (2 + 2 )(2  2 )
 75.16: 1 + 5 3  5 1
 75.17: 4  7 3 + 7
 75.18: 243 1
 75.19: 72 20
 75.20: 54 21
 75.21: 96
 75.22: 50 x 4
 75.23: 16 y 3
 75.24: 18 x 2 y 3 25.
 75.25: 40 a 3 b 4
 75.26: 3 3 56 y 6 z 3 27.
 75.27: 2 3 24 m 4 n 5 2
 75.28: 4 _1 81c 5 d 4 29.
 75.29: 5 _1 32w 6 z 7 30.
 75.30: 3 _3 4
 75.31: 4 _2 3
 75.32: a 4 _ b 3
 75.33: 4 r _ 8 t 9 3
 75.34: (3 12 )(2 21 ) 35.
 75.35: (3 24 )(5 20 )
 75.36: GEOMETRY Find the perimeter and area of the rectangle.
 75.37: GEOMETRY Find the perimeter of a regular pentagon whose sides measu...
 75.38: 12 + 48  27 39.
 75.39: 98  72 + 32 40
 75.40: 3 + 72  128 + 108 41. 5
 75.41: 5 20 + 24  180 + 7 54 42.
 75.42: (5 + 6 )(5  2 ) 43.
 75.43: (3 + 7 )(2 + 6 )
 75.44: (11  2 )2 45.
 75.45: (3  5 )2
 75.46: 7 4  3
 75.47: 6 5 + 3
 75.48: 2  3 1 + 3
 75.49: 2 + 2 5  2 50
 75.50: x + 1 x 2  1 5
 75.51: x  1 x  1
 75.52: What is 39 divided by 26 ? 5
 75.53: Divide 14 by 35 .
 75.54: Explain why v 0 = v  8 h is not equivalent to the given formula.
 75.55: What velocity must a coaster have at the top of a 225foot hill to ...
 75.56: Use the properties of radicals to rewrite the formula.
 75.57: How far will a ball that is hit with a velocity of 45 meters per se...
 75.58: REASONING Determine whether the statement _1 n a = n a is sometimes...
 75.59: REASONING Determine whether the statement _1 n a = n a is sometimes...
 75.60: FIND THE ERROR Ethan and Alexis are simplifying _4 + 5 2  5 . Who ...
 75.61: Writing in Math Refer to the information given on page 408 to expla...
 75.62: ACT/SAT The expression 180 a 2 b 8is equivalent to which of the fol...
 75.63: REVIEW When the number of a year is divisible by 4, then a leap yea...
 75.64: 144 z 8
 75.65: 3 216 a 3b 9 66
 75.66: (y + 2)2 67.
 75.67: Graph y x + 1 . (Le
 75.68: ELECTRONICS There are three basic things to be considered in an ele...
 75.69: 8 7 6 5
 75.70: 1 1 2 3
 75.71: 8 6 4 3
 75.72: 2 (_1 8)
 75.73: 3 (_1 6)
 75.74: 1 2 + _1 3
 75.75: 1 3 + _3 4
 75.76: 1 8 + _5 12
 75.77: 5 6  _1 5
 75.78: 5 8  _1 4
 75.79: 1 4  _2 3
Solutions for Chapter 75: Operations with Radical Expressions
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 75: Operations with Radical Expressions
Get Full SolutionsSince 79 problems in chapter 75: Operations with Radical Expressions have been answered, more than 56585 students have viewed full stepbystep solutions from this chapter. Chapter 75: Operations with Radical Expressions includes 79 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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).

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.