13.1.8: Chapter 8

Last updated
Save as PDF

Page ID: 117743

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $

$ \newcommand{\dsum}{\displaystyle\sum\limits} $

$ \newcommand{\dint}{\displaystyle\int\limits} $

$ \newcommand{\dlim}{\displaystyle\lim\limits} $

$ \newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$

( \newcommand{\kernel}{\mathrm{null}\,}\) $ \newcommand{\range}{\mathrm{range}\,}$

$ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$

$ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$

$ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$ \newcommand{\Span}{\mathrm{span}}$

$ \newcommand{\id}{\mathrm{id}}$

$ \newcommand{\Span}{\mathrm{span}}$

$ \newcommand{\kernel}{\mathrm{null}\,}$

$ \newcommand{\range}{\mathrm{range}\,}$

$ \newcommand{\RealPart}{\mathrm{Re}}$

$ \newcommand{\ImaginaryPart}{\mathrm{Im}}$

$ \newcommand{\Argument}{\mathrm{Arg}}$

$ \newcommand{\norm}[1]{\| #1 \|}$

$ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\AA}{\unicode[.8,0]{x212B}}$

$ \newcommand{\vectorA}[1]{\vec{#1}} % arrow$

$ \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$

$ \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vectorC}[1]{\textbf{#1}} $

$ \newcommand{\vectorD}[1]{\overrightarrow{#1}} $

$ \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} $

$ \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} $

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$\newcommand{\longvect}{\overrightarrow}$

$ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $

$\newcommand{\ket}[1]{\left| #1 \right>}$
$\newcommand{\bra}[1]{\left< #1 \right|}$
$\newcommand{\braket}[2]{\left< #1 \vphantom{#2} \right| \left. #2 \vphantom{#1} \right>}$
$\newcommand{\braopket}[3]{\left< #1 \vphantom{#2}\vphantom{#3} \right| #2 \vphantom{#1}\vphantom{#3} \left| #3 \vphantom{#1}\vphantom{#2} \right>}$
$\newcommand{\qmvec}[1]{\mathbf{\vec{#1}}}$
$\newcommand{\op}[1]{\hat{\mathbf{#1}}}$
$\newcommand{\expect}[1]{\langle #1 \rangle}$
$\newcommand{\dfn}[1]{\emph{\textbf{#1}}}$

$\newcommand{\avec}{\mathbf a}$ $\newcommand{\bvec}{\mathbf b}$ $\newcommand{\cvec}{\mathbf c}$ $\newcommand{\dvec}{\mathbf d}$ $\newcommand{\dtil}{\widetilde{\mathbf d}}$ $\newcommand{\evec}{\mathbf e}$ $\newcommand{\fvec}{\mathbf f}$ $\newcommand{\nvec}{\mathbf n}$ $\newcommand{\pvec}{\mathbf p}$ $\newcommand{\qvec}{\mathbf q}$ $\newcommand{\svec}{\mathbf s}$ $\newcommand{\tvec}{\mathbf t}$ $\newcommand{\uvec}{\mathbf u}$ $\newcommand{\vvec}{\mathbf v}$ $\newcommand{\wvec}{\mathbf w}$ $\newcommand{\xvec}{\mathbf x}$ $\newcommand{\yvec}{\mathbf y}$ $\newcommand{\zvec}{\mathbf z}$ $\newcommand{\rvec}{\mathbf r}$ $\newcommand{\mvec}{\mathbf m}$ $\newcommand{\zerovec}{\mathbf 0}$ $\newcommand{\onevec}{\mathbf 1}$ $\newcommand{\real}{\mathbb R}$ $\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$ $\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$ $\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$ $\newcommand{\laspan}[1]{\text{Span}\{#1\}}$ $\newcommand{\bcal}{\cal B}$ $\newcommand{\ccal}{\cal C}$ $\newcommand{\scal}{\cal S}$ $\newcommand{\wcal}{\cal W}$ $\newcommand{\ecal}{\cal E}$ $\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$ $\newcommand{\gray}[1]{\color{gray}{#1}}$ $\newcommand{\lgray}[1]{\color{lightgray}{#1}}$ $\newcommand{\rank}{\operatorname{rank}}$ $\newcommand{\row}{\text{Row}}$ $\newcommand{\col}{\text{Col}}$ $\renewcommand{\row}{\text{Row}}$ $\newcommand{\nul}{\text{Nul}}$ $\newcommand{\var}{\text{Var}}$ $\newcommand{\corr}{\text{corr}}$ $\newcommand{\len}[1]{\left|#1\right|}$ $\newcommand{\bbar}{\overline{\bvec}}$ $\newcommand{\bhat}{\widehat{\bvec}}$ $\newcommand{\bperp}{\bvec^\perp}$ $\newcommand{\xhat}{\widehat{\xvec}}$ $\newcommand{\vhat}{\widehat{\vvec}}$ $\newcommand{\uhat}{\widehat{\uvec}}$ $\newcommand{\what}{\widehat{\wvec}}$ $\newcommand{\Sighat}{\widehat{\Sigma}}$ $\newcommand{\lt}{<}$ $\newcommand{\gt}{>}$ $\newcommand{\amp}{&}$ $\definecolor{fillinmathshade}{gray}{0.9}$

Be Prepared

8.1

ⓐ 8; ⓑ −1; ⓒ-729

8.2

3.85

8.3

ⓐ $x^{6}$ ; ⓑ $y^{6}$ ; ⓒ $z^{12}$

8.4

$x^{5}$

8.5

$\frac{1}{y^{8}}$

8.6

$n^{12}$

8.7

$\frac{53}{60}$

8.8

$64 x^{6} y^{15}$

8.9

$\frac{1}{125}$

8.10

$2 x^{2} + 11 x - 8$

8.11

$8 + 2 a - a^{2}$

8.12

$81 - 90 y + 25 y^{2}$

8.13

$\frac{5}{8}$

8.14

$x^{6}$

8.15

$49 - 9 x^{2}$

8.16

$y^{2} - 6 y + 9$

8.17

$x = \frac{5}{2}$

8.18

$n = 2 or n = 4$

8.19

$(− \infty, \frac{1}{2}]$

8.20

$f (2) = 2, f (−1) = −7, f (0) = −4$

8.21

$domain: [0, \infty); range: [0, \infty)$

8.22

ⓐ $−4, 0. \bar{5}, \frac{7}{3}, 3, \sqrt{81};$ ⓑ $\sqrt{7};$ ⓒ $−4, - \sqrt{7}, 0. \bar{5}, \frac{7}{3}, 3, \sqrt{81}$

8.23

$2 x^{2} - x - 15$

8.24

$\frac{\sqrt{5} (\sqrt{15})}{2}$

Try It

8.1

ⓐ $−8$ ⓑ 15

8.2

ⓐ 10 ⓑ $−11$

8.3

ⓐ not a real number ⓑ $−9$

8.4

ⓐ $−7$ ⓑ not a real number

8.5

ⓐ 3 ⓑ 4 ⓒ 3

8.6

ⓐ 10 ⓑ 2 ⓒ 4

8.7

ⓐ $−3$ ⓑ not real ⓒ $−2$

8.8

ⓐ $−6$ ⓑ not real ⓒ $−4$

8.9

ⓐ $6 < \sqrt{38} < 7$
ⓑ $4 < \sqrt[3]{93} < 5$

8.10

ⓐ $9 < \sqrt{84} < 10$
ⓑ $5 < \sqrt[3]{152} < 6$

8.11

ⓐ $\approx 3.32$ ⓑ $\approx 4.14$
ⓒ $\approx 3.36$

8.12

ⓐ $\approx 3.61$ ⓑ $\approx 4.38$
ⓒ $\approx 3.15$

8.13

ⓐ $| b |$ ⓑ w ⓒ $| m |$ ⓓ q

8.14

ⓐ $| y |$ ⓑ p ⓒ $| z |$ ⓓ q

8.15

ⓐ $| y^{9} |$ ⓑ $z^{6}$

8.16

ⓐ $m^{2}$ ⓑ $| b^{5} |$

8.17

ⓐ $| u^{3} |$ ⓑ $v^{5}$

8.18

ⓐ $c^{4}$ ⓑ $d^{4}$

8.19

ⓐ $8 | x |$ ⓑ $−10 | p |$

8.20

ⓐ $13 | y |$ ⓑ $−11 | y |$

8.21

ⓐ $3 x^{9}$ ⓑ $3 | q^{7} |$

8.22

ⓐ $5 q^{3}$ ⓑ $3 q^{5}$

8.23

ⓐ $10 | a b |$ ⓑ $12 p^{6} q^{10}$
ⓒ $2 x^{10} y^{4}$

8.24

ⓐ $15 | m n |$ ⓑ $13 | x^{5} y^{7} |$
ⓒ $3 w^{12} z^{5}$

8.25

$4 \sqrt{3}$

8.26

$3 \sqrt{5}$

8.27

ⓐ $12 \sqrt{2}$ ⓑ $3 \sqrt[3]{3}$ ⓒ $2 \sqrt[4]{4}$

8.28

ⓐ $12 \sqrt{3}$ ⓑ $5 \sqrt[3]{5}$ ⓒ $3 \sqrt[4]{9}$

8.29

ⓐ $b^{2} \sqrt{b}$ ⓑ $| y | \sqrt[4]{y^{2}}$ ⓒ $z \sqrt[3]{z^{2}}$

8.30

ⓐ $p^{4} \sqrt{p}$ ⓑ $y \sqrt[5]{y^{3}}$
ⓒ $q^{2} \sqrt[6]{q}$

8.31

ⓐ $4 y^{2} \sqrt{2 y}$ ⓑ $3 p^{3} \sqrt[3]{2 p}$
ⓒ $2 q^{2} \sqrt[4]{4 q^{2}}$

8.32

ⓐ $5 a^{4} \sqrt{3 a}$ ⓑ $4 m^{3} \sqrt[3]{2 m^{2}}$
ⓒ $3 | n | \sqrt[4]{2 n^{3}}$

8.33

ⓐ $7 | a^{3} | b^{2} {\sqrt{2 a b}}^{}$
ⓑ $2 x y \sqrt[3]{7 x^{2} y}$ ⓒ $2 | x | y^{2} \sqrt[4]{2 x}$

8.34

ⓐ $6 m^{4} | n^{5} | \sqrt{5 m n}$
ⓑ $2 x^{2} y \sqrt[3]{9 y^{2}}$ ⓒ $2 | x y | \sqrt[4]{5 x^{3}}$

8.35

ⓐ $−4$ ⓑ $no real number$

8.36

ⓐ $−5 \sqrt[3]{5}$ ⓑ no real number

8.37

ⓐ $5 + 5 \sqrt{3}$ ⓑ $2 - \sqrt{3}$

8.38

ⓐ $2 + 7 \sqrt{2}$ ⓑ $2 - \sqrt{5}$

8.39

ⓐ $\frac{5}{4}$ ⓑ $\frac{3}{5}$ ⓒ $\frac{2}{3}$

8.40

ⓐ $\frac{7}{9}$ ⓑ $\frac{2}{5}$ ⓒ $\frac{1}{3}$

8.41

ⓐ $| a |$ ⓑ $| x |$ ⓒ $y^{3}$

8.42

ⓐ $x^{2}$ ⓑ $m^{2}$ ⓒ $n^{2}$

8.43

$\frac{2 | p | \sqrt{6 p}}{7}$

8.44

$\frac{2 x^{2} \sqrt{3 x}}{5}$

8.45

ⓐ $\frac{4 | m | \sqrt{5 m}}{| n^{3} |}$ ⓑ $\frac{3 c^{3} \sqrt[3]{4 c}}{d^{2}}$
ⓒ $\frac{2 x^{2} \sqrt[4]{5 x^{2}}}{| y |}$

8.46

ⓐ $\frac{3 u^{3} \sqrt{6 u}}{v^{4}}$ ⓑ $\frac{2 r \sqrt[3]{5}}{s^{2}}$
ⓒ $\frac{3 | m^{3} | \sqrt[4]{2 m^{2}}}{| n^{3} |}$

8.47

ⓐ $\frac{5 | y | \sqrt{x}}{6}$ ⓑ $\frac{2 x y \sqrt[3]{y^{2}}}{3}$
ⓒ $\frac{| a b | \sqrt[4]{a}}{2}$

8.48

ⓐ $\frac{2 | m | \sqrt{3}}{5 | n^{3} |}$ ⓑ $\frac{3 x y \sqrt[3]{x^{2}}}{5}$
ⓒ $\frac{2 | a b | \sqrt[4]{a^{2}}}{3}$

8.49

ⓐ $7 z^{2}$ ⓑ $−5 \sqrt[3]{2}$
ⓒ $3 | m | \sqrt[4]{2 m^{2}}$

8.50

ⓐ $8 m^{4}$ ⓑ $−4$ ⓒ $3 | n | \sqrt[4]{2}$

8.51

ⓐ $\sqrt{t}$ ⓑ $\sqrt[3]{m}$ ⓒ $\sqrt[4]{r}$

8.52

ⓐ $\sqrt[6]{b}$ ⓑ $\sqrt[5]{z}$ ⓒ $\sqrt[4]{p}$

8.53

ⓐ ${(10 m)}^{\frac{1}{2}}$ ⓑ ${(3 n)}^{\frac{1}{5}}$
ⓒ $3 {(6 y)}^{\frac{1}{4}}$

8.54

ⓐ ${(3 k)}^{\frac{1}{7}}$ ⓑ ${(5 j)}^{\frac{1}{4}}$
ⓒ $8 {(2 a)}^{\frac{1}{3}}$

8.55

ⓐ 6 ⓑ 2 ⓒ 2

8.56

ⓐ 10 ⓑ 3 ⓒ 3

8.57

ⓐ No real solution ⓑ $−8$
ⓒ $\frac{1}{8}$

8.58

ⓐ No real solution ⓑ $−4$
ⓒ $\frac{1}{4}$

8.59

ⓐ $x^{\frac{5}{2}}$ ⓑ ${(3 y)}^{\frac{3}{4}}$ ⓒ ${(\frac{2 m}{3 n})}^{\frac{5}{2}}$

8.60

ⓐ $a^{\frac{2}{5}}$ ⓑ ${(5 a b)}^{\frac{5}{3}}$
ⓒ ${(\frac{7 x y}{z})}^{\frac{3}{2}}$

8.61

ⓐ 9 ⓑ $\frac{1}{729}$ ⓒ $\frac{1}{8}$

8.62

ⓐ 8 ⓑ $\frac{1}{9}$ ⓒ $\frac{1}{125}$

8.63

ⓐ $−64$ ⓑ $- \frac{1}{64}$ ⓒ not a real number

8.64

ⓐ $−729$ ⓑ $- \frac{1}{729}$ ⓒ not a real number

8.65

ⓐ $x^{\frac{3}{2}}$ ⓑ $x^{8}$ ⓒ $\frac{1}{x}$

8.66

ⓐ $y^{\frac{11}{8}}$ ⓑ $m^{2}$ ⓒ $\frac{1}{d}$

8.67

ⓐ $8 x^{\frac{1}{5}}$ ⓑ $x^{\frac{1}{2}} y^{\frac{1}{3}}$

8.68

ⓐ $729 n^{\frac{3}{5}}$ ⓑ $a^{2} b^{\frac{2}{3}}$

8.69

ⓐ $m^{2}$ ⓑ $\frac{5 n}{m^{\frac{1}{4}}}$

8.70

ⓐ $u^{3}$ ⓑ $3 x^{\frac{1}{5}} y^{\frac{1}{3}}$

8.71

ⓐ $− \sqrt{2}$ ⓑ $11 \sqrt[3]{x}$
ⓒ $3 \sqrt[4]{x} - 5 \sqrt[4]{y}$

8.72

ⓐ $−4 \sqrt{3}$ ⓑ $8 \sqrt[3]{y}$
ⓒ $5 \sqrt[4]{m} - 2 \sqrt[3]{m}$

8.73

ⓐ $−2 \sqrt{7 x}$ ⓑ $− \sqrt[4]{5 x y}$

8.74

ⓐ $− \sqrt{3 y}$ ⓑ $3 \sqrt[3]{7 m n}$

8.75

ⓐ $9 \sqrt{2}$ ⓑ $2 \sqrt[3]{2}$ ⓒ $\sqrt[3]{3}$

8.76

ⓐ $7 \sqrt{3}$ ⓑ $−10 \sqrt[3]{5}$ ⓒ $−3 \sqrt[3]{2}$

8.77

ⓐ $− m^{3} \sqrt{2 m}$ ⓑ $x^{2} \sqrt[3]{5 x}$

8.78

ⓐ $− p \sqrt{3 p}$
ⓑ $4 y \sqrt[3]{4 y^{2}} - 2 n \sqrt[3]{4 n^{2}}$

8.79

ⓐ $12 \sqrt{15}$ ⓑ $−18 \sqrt[3]{4}$

8.80

ⓐ $27 \sqrt{2}$ ⓑ $−36 \sqrt[3]{2}$

8.81

ⓐ $288 x^{3} \sqrt{5}$ ⓑ $8 y \sqrt[4]{6 y^{2}}$

8.82

ⓐ $144 y^{2} \sqrt{5 y}$ ⓑ $−36 a \sqrt[4]{3 a}$

8.83

ⓐ $18 + \sqrt{6}$ ⓑ $−2 \sqrt[3]{4} - 2 \sqrt[3]{3}$

8.84

ⓐ $−40 + 4 \sqrt{2}$ ⓑ $−3 - \sqrt[3]{18}$

8.85

ⓐ $−66 + 15 \sqrt{7}$
ⓑ $\sqrt[3]{x^{2}} - 5 \sqrt[3]{x} + 6$

8.86

ⓐ $41 - 14 \sqrt{11}$
ⓑ $\sqrt[3]{x^{2}} + 4 \sqrt[3]{x} + 3$

8.87

$1 + 9 \sqrt{21}$

8.88

$−12 - 20 \sqrt{3}$

8.89

ⓐ $102 + 20 \sqrt{2}$ ⓑ $55 + 6 \sqrt{6}$

8.90

ⓐ $41 - 12 \sqrt{5}$
ⓑ $121 - 36 \sqrt{10}$

8.91

$−11$

8.92

$−159$

8.93

ⓐ $\frac{5 s}{8}$ ⓑ $\frac{2}{a}$

8.94

ⓐ $\frac{5 q^{2}}{6}$ ⓑ $\frac{2}{b}$

8.95

ⓐ $\frac{9 x^{2}}{y^{2}}$ ⓑ $\frac{−4 x}{y}$

8.96

ⓐ $\frac{10 n^{3}}{m}$ ⓑ $\frac{−3 p}{q^{2}}$

8.97

$4 x y \sqrt{2 x}$

8.98

$4 a b \sqrt{3 b}$

8.99

ⓐ $\frac{5 \sqrt{3}}{3}$ ⓑ $\frac{\sqrt{6}}{8}$ ⓒ $\frac{\sqrt{2 x}}{x}$

8.100

ⓐ $\frac{6 \sqrt{5}}{5}$ ⓑ $\frac{\sqrt{14}}{6}$ ⓒ $\frac{\sqrt{5 x}}{x}$

8.101

ⓐ $\frac{\sqrt[3]{49}}{7}$ ⓑ $\frac{\sqrt[3]{90}}{6}$ ⓒ $\frac{5 \sqrt[3]{3 y^{2}}}{3 y}$

8.102

ⓐ $\frac{\sqrt[3]{4}}{2}$ ⓑ $\frac{\sqrt[3]{150}}{10}$ ⓒ $\frac{2 \sqrt[3]{5 n^{2}}}{5 n}$

8.103

ⓐ $\frac{\sqrt[4]{27}}{3}$ ⓑ $\frac{\sqrt[4]{12}}{4}$ ⓒ $\frac{3 \sqrt[4]{5 x^{3}}}{5 x}$

8.104

ⓐ $\frac{\sqrt[4]{125}}{5}$ ⓑ $\frac{\sqrt[4]{14}}{4}$
ⓒ $\frac{2 \sqrt[4]{4 x^{3}}}{x}$

8.105

$- \frac{3 (1 + \sqrt{5})}{4}$

8.106

$\frac{4 + \sqrt{6}}{5}$

8.107

$\frac{\sqrt{5} (\sqrt{x} - \sqrt{2})}{x - 2}$

8.108

$\frac{\sqrt{10} (\sqrt{y} + \sqrt{3})}{y - 3}$

8.109

${\frac{(\sqrt{p} + \sqrt{2})}{p - 2}}^{2}$

8.110

${\frac{(\sqrt{q} - \sqrt{10})}{q - 10}}^{2}$

8.111

$m = \frac{23}{3}$

8.112

$z = \frac{3}{10}$

8.113

$no solution$

8.114

$no solution$

8.115

$x = 2, x = 3$

8.116

$y = 5, y = 6$

8.117

$x = −6$

8.118

$x = −9$

8.119

$x = 8$

8.120

$x = 6$

8.121

$m = 7$

8.122

$n = 3$

8.123

$a = 63$

8.124

$b = 311$

8.125

$x = 3$

8.126

$x = - \frac{6}{5}$

8.127

$x = 4$

8.128

$x = 9$

8.129

$x = 5$

8.130

$x = 0 x = 4$

8.131

9 seconds

8.132

$3.5$ seconds

8.133

$42.7$ feet

8.134

$54.1$ feet

8.135

ⓐ $f (6) = 4$ ⓑ no value at $x = 0$

8.136

ⓐ $g (4) = 5$ ⓑ no value at $f (−3)$

8.137

ⓐ $g (4) = 2$ ⓑ $g (1) = −1$

8.138

ⓐ $h (2) = 2$
ⓑ $h (−5) = −3$

8.139

ⓐ $f (4) = 2$ ⓑ $f (−1) = 1$

8.140

ⓐ $g (16) = 3$ ⓑ $g (3) = 2$

8.141

$[\frac{5}{6}, \infty)$

8.142

$(− \infty, \frac{4}{5}]$

8.143

$(−3, \infty)$

8.144

$(5, \infty)$

8.145

$(− \infty, \infty)$

8.146

$(− \infty, \infty)$

8.147

ⓐ domain: $[−2, \infty)$
ⓑ

$The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 6. The y-axis runs from 0 to 8. The function has a starting point at (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).$

8.148

ⓐ domain: $[2, \infty)$
ⓑ

$The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 6. The function has a starting point at (2, 0) and goes through the points (3, 1) and (6, 2).$

8.149

ⓐ domain: $(- \infty, \infty)$
ⓑ

$The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 2. The y-axis runs from negative 2 to 2. The function has a center point at (0, 0) and goes through the points (1, negative 1) and (negative 1, 1).$

8.150

ⓐ domain: $(- \infty, \infty)$
ⓑ

$The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 5. The y-axis runs from negative 3 to 3. The function has a center point at (2, 0) and goes through the points (1, negative 1) and (3, 2).$

8.151

ⓐ $9 i$ ⓑ $\sqrt{5} i$ ⓒ $3 \sqrt{2} i$

8.152

ⓐ $6 i$ ⓑ $\sqrt{3} i$ ⓒ $3 \sqrt{3} i$

8.153

$6 \sqrt{2} i$

8.154

$7 \sqrt{3} i$

8.155

ⓐ $6 + 5 i$ ⓑ $6 - 3 i$

8.156

ⓐ $−2 - 6 i$ ⓑ $2 + 9 i$

8.157

$12 + 20 i$

8.158

$12 - 6 i$

8.159

$−11 - 7 i$

8.160

$−5 - 10 i$

8.161

$−21 - 20 i$

8.162

$9 - 40 i$

8.163

$−14$

8.164

$−54$

8.165

$−12 - 22 \sqrt{3} i$

8.166

$6 + 12 \sqrt{2} i$

8.167

8.168

8.169

109

8.170

8.171

8.172

8.173

$\frac{4}{17} + \frac{16}{17} i$

8.174

$\frac{2}{5} + \frac{4}{5} i$

8.175

$\frac{3}{2} - \frac{3}{2} i$

8.176

$\frac{4}{5} - \frac{2}{5} i$

8.177

$− i$

8.178

$1$

Section 8.1 Exercises

ⓐ 8 ⓑ $−9$

ⓐ 14 ⓑ $−1$

ⓐ $\frac{2}{3}$ ⓑ $−0.1$

ⓐ not real number ⓑ $−17$

ⓐ $−15$ ⓑ not real number

11.

ⓐ 6 ⓑ 4

13.

ⓐ 8 ⓑ 3 ⓒ 1

15.

ⓐ $−2$ ⓑ $not real$ ⓒ $−2$

17.

ⓐ $−5$ ⓑ $not real$ ⓒ $−4$

19.

ⓐ $8 < \sqrt{70} < 9$
ⓑ $4 < \sqrt[3]{71} < 5$

21.

ⓐ $14 < \sqrt{200} < 15$
ⓑ $5 < \sqrt[3]{137} < 6$

23.

ⓐ $\approx 4.36$ ⓑ $\approx 4.46$
ⓒ $\approx 3.14$

25.

ⓐ $\approx 7.28$ ⓑ $\approx 5.28$
ⓒ $\approx 4.61$

27.

ⓐ u ⓑ $| v |$

29.

ⓐ $| y |$ ⓑ $m$

31.

ⓐ $| x^{3} |$ ⓑ $y^{8}$

33.

ⓐ $x^{12}$ ⓑ $| y^{11} |$

35.

ⓐ $x^{3}$ ⓑ $| y^{3} |$

37.

ⓐ $m^{2}$ ⓑ $n^{4}$

39.

ⓐ $7 | x |$ ⓑ $−9 | x^{9} |$

41.

ⓐ $11 m^{10}$ ⓑ $−8 | a |$

43.

ⓐ $2 x^{2}$ ⓑ $2 y^{2}$

45.

ⓐ $6 a^{2}$ ⓑ $2 b^{4}$

47.

ⓐ $12 | x y |$ ⓑ $13 w^{4} | y^{5} |$
ⓒ $2 a^{17} b^{2}$

49.

ⓐ $11 | a b |$ ⓑ $3 c^{4} d^{6}$
ⓒ $4 x^{5} y^{22}$

51.

Answers will vary.

53.

Answers will vary.

Section 8.2 Exercises

55.

$3 \sqrt{3}$

57.

$5 \sqrt{5}$

59.

$7 \sqrt{3}$

61.

$20 \sqrt{2}$

63.

ⓐ $2 \sqrt[4]{2}$ ⓑ $2 \sqrt[5]{2}$

65.

ⓐ $2 \sqrt[4]{4}$ ⓑ $4 \sqrt[3]{4}$

67.

ⓐ $| y^{5} | \sqrt[]{y}$ ⓑ $r \sqrt[3]{r^{2}}$ ⓒ $s^{2} \sqrt[4]{s^{2}}$

69.

ⓐ $n^{10} \sqrt{n}$ ⓑ $q^{2} \sqrt[3]{q^{2}}$
ⓒ $| n | \sqrt[8]{n^{2}}$

71.

ⓐ $5 r^{6} \sqrt[]{5 r}$ ⓑ $3 x \sqrt[3]{4 x^{2}}$
ⓒ $2 | y | \sqrt[4]{3 y^{2}}$

73.

ⓐ $11 | m^{11} | \sqrt[]{2 m}$ ⓑ $3 m^{2} \sqrt[4]{5 m^{2}}$ ⓒ $2 n \sqrt[5]{5 n^{3}}$

75.

ⓐ $7 | m^{3} n^{5} | \sqrt[]{3 m n}$ ⓑ $2 x^{2} y^{2} \sqrt[3]{6 y}$ ⓒ $2 | x y | \sqrt[4]{2 x}$

77.

ⓐ $8 | q r^{3} | \sqrt{3 q r}$ ⓑ $3 m^{3} n^{3} \sqrt[3]{2 n}$ ⓒ $3 a^{2} b^{2} \sqrt[4]{a}$

79.

ⓐ $−6 \sqrt[3]{4}$ ⓑ not real

81.

ⓐ $−2$ ⓑ not real

83.

ⓐ $5 + 2 \sqrt{3}$ ⓑ $5 - \sqrt{6}$

85.

ⓐ $1 + 3 \sqrt{5}$ ⓑ $1 + \sqrt{10}$

87.

ⓐ $\frac{3}{4}$ ⓑ $\frac{2}{3}$ ⓒ $\frac{1}{3}$

89.

ⓐ $\frac{5}{3}$ ⓑ $\frac{3}{5}$ ⓒ $\frac{1}{4}$

91.

ⓐ $x^{2}$ ⓑ $p^{3}$ ⓒ $| q |$

93.

ⓐ $\frac{1}{y^{2}}$ ⓑ $u^{2}$ ⓒ $| v^{3} |$

95.

$\frac{4 | x^{3} | \sqrt{6 x}}{11}$

97.

$\frac{5 m^{2} \sqrt{3 m}}{4}$

99.

$\frac{7 r^{2} \sqrt{2 r}}{10}$

101.

$\frac{2 | q^{3} | \sqrt{7}}{15}$

103.

ⓐ $\frac{5 r^{4} \sqrt{3 r}}{s^{4}}$ ⓑ $\frac{3 a^{2} \sqrt[3]{2 a^{2}}}{b}$
ⓒ $\frac{2 | c | \sqrt[4]{4 c}}{| d |}$

105.

ⓐ $\frac{2 | p^{3} | \sqrt{7 p}}{| q |}$ ⓑ $\frac{3 s^{2} \sqrt[3]{3 s^{2}}}{t}$
ⓒ $\frac{2 | p^{3} | \sqrt[4]{4 p^{3}}}{| q^{3} |}$

107.

ⓐ $\frac{4 | x y |}{3}$ ⓑ $\frac{y^{2} \sqrt[3]{x}}{2}$ ⓒ $\frac{| a b | \sqrt[4]{a}}{2}$

109.

ⓐ $\frac{1}{2 | p q |}$ ⓑ $\frac{2 c d \sqrt[3]{d^{2}}}{5}$
ⓒ $\frac{| m n |}{2}$

111.

ⓐ $\frac{3 p^{4} \sqrt{p}}{| q |}$ ⓑ $2 \sqrt[4]{2}$
ⓒ $2 x \sqrt[5]{2 x}$

113.

ⓐ $5 | m^{3} |$ ⓑ $5 \sqrt[3]{5}$
ⓒ $3 | y | \sqrt[4]{3 y^{2}}$

115.

Answers will vary.

117.

Answers will vary.

Section 8.3 Exercises

119.

ⓐ $\sqrt{x}$ ⓑ $\sqrt[3]{y}$ ⓒ $\sqrt[4]{z}$

121.

ⓐ $\sqrt[5]{u}$ ⓑ $\sqrt[9]{v}$ ⓒ $\sqrt[20]{w}$

123.

ⓐ $x^{\frac{1}{7}}$ ⓑ $y^{\frac{1}{9}}$ ⓒ $f^{\frac{1}{5}}$

125.

ⓐ ${(7 c)}^{\frac{1}{3}}$ ⓑ ${(12 d)}^{\frac{1}{7}}$
ⓒ $2 {(6 b)}^{\frac{1}{4}}$

127.

ⓐ ${(21 p)}^{\frac{1}{2}}$ ⓑ ${(8 q)}^{\frac{1}{4}}$
ⓒ $4 {(36 r)}^{\frac{1}{6}}$

129.

ⓐ 9 ⓑ 5 ⓒ 8

131.

ⓐ 2 ⓑ 4 ⓒ 5

133.

ⓐ $−6$ ⓑ $−6$ ⓒ $\frac{1}{6}$

135.

ⓐ not real ⓑ $−3$ ⓒ $\frac{1}{3}$

137.

ⓐ not real ⓑ $−6$ ⓒ $\frac{1}{6}$

139.

ⓐ not real ⓑ $−10$ ⓒ $\frac{1}{10}$

141.

ⓐ $m^{\frac{5}{2}}$ ⓑ ${(3 y)}^{\frac{7}{3}}$ ⓒ ${(\frac{4 x}{5 y})}^{\frac{3}{5}}$

143.

ⓐ $u^{\frac{2}{5}}$ ⓑ ${(6 x)}^{\frac{5}{3}}$ ⓒ ${(\frac{18 a}{5 b})}^{\frac{7}{4}}$

145.

ⓐ 32,768 ⓑ $\frac{1}{729}$ ⓒ 9

147.

ⓐ 4 ⓑ $\frac{1}{9}$ ⓒ not real

149.

ⓐ $−27$ ⓑ $- \frac{1}{27}$ ⓒ not real

151.

ⓐ $c^{\frac{7}{8}}$ ⓑ $p^{9}$ ⓒ $\frac{1}{r}$

153.

ⓐ $y^{\frac{5}{4}}$ ⓑ $x^{8}$ ⓒ $\frac{1}{m}$

155.

ⓐ $81 q^{2}$ ⓑ $a^{\frac{1}{2}} b$

157.

ⓐ $8 u^{\frac{1}{4}}$ ⓑ $8 p^{\frac{1}{2}} q^{\frac{3}{4}}$

159.

ⓐ $r^{\frac{7}{2}}$ ⓑ $\frac{6 s}{t}$

161.

ⓐ $c^{2}$ ⓑ $\frac{2 x}{3 y}$

163.

Answers will vary.

Section 8.4 Exercises

165.

ⓐ $3 \sqrt{2}$ ⓑ $7 \sqrt[3]{m}$ ⓒ $6 \sqrt[4]{m}$

167.

ⓐ $9 \sqrt{5}$ ⓑ $12 \sqrt[3]{a}$ ⓒ $6 \sqrt[4]{2 z}$

169.

ⓐ $4 \sqrt{2 a}$ ⓑ 0

171.

ⓐ $\sqrt{3 c}$ ⓑ $\sqrt[3]{4 p q}$

173.

ⓐ $−2 \sqrt{3}$ ⓑ $−2 \sqrt[3]{5}$ ⓒ $3 \sqrt[4]{2}$

175.

ⓐ $7 \sqrt{3}$ ⓑ $7 \sqrt[3]{2}$ ⓒ $3 \sqrt[4]{5}$

177.

ⓐ $a^{2} \sqrt{2 a}$ ⓑ 0

179.

ⓐ $2 c^{3} \sqrt{5 c}$ ⓑ $14 r^{2} \sqrt[4]{2 r^{2}}$

181.

$4 y \sqrt{2}$

183.

ⓐ $−18 \sqrt{6}$ ⓑ $−64 \sqrt[3]{9}$

185.

ⓐ $−30 \sqrt{2}$ ⓑ $6 \sqrt[4]{2}$

187.

ⓐ $72 z^{2} \sqrt{3}$ ⓑ $45 x^{2} \sqrt[3]{2}$

189.

ⓐ $−42 z^{5} \sqrt{2 z}$ ⓑ $−8 y \sqrt[4]{6 y}$

191.

ⓐ $14 + 5 \sqrt{7}$ ⓑ $4 \sqrt[3]{6} + 3 \sqrt[3]{4}$

193.

ⓐ $44 - 3 \sqrt{11}$ ⓑ $3 \sqrt[4]{2} + \sqrt[4]{54}$

195.

$60 + 2 \sqrt{3}$

197.

ⓐ $30 + 18 \sqrt{2}$ ⓑ $\sqrt[3]{x^{2}} - 2 \sqrt[3]{x} - 3$

199.

ⓐ $−55 + 13 \sqrt{10}$
ⓑ $2 \sqrt[3]{x^{2}} + 8 \sqrt[3]{x} + 6$

201.

$23 + 3 \sqrt{30}$

203.

$−439 - 2 \sqrt{77}$

205.

ⓐ $14 + 6 \sqrt{5}$ ⓑ $79 - 20 \sqrt{3}$

207.

ⓐ $87 - 18 \sqrt{6}$
ⓑ $163 + 60 \sqrt{7}$

209.

211.

$−227$

213.

$19$

215.

$\sqrt[3]{9 x^{2}} - 4$

217.

$5 \sqrt{3}$

219.

$9 \sqrt{2}$

221.

$− \sqrt[4]{5}$

223.

$10 c^{2} \sqrt{3} - 9 c^{3} \sqrt{3}$

225.

$2 \sqrt{3}$

227.

$17 q^{2}$

229.

$3 \sqrt{7}$

231.

$−42 \sqrt[3]{9}$

233.

235.

$29 - 7 \sqrt{17}$

237.

$54 - 36 \sqrt{2}$

239.

$6 + 3 \sqrt[3]{2}$

241.

Answers will vary.

243.

Answers will vary.

Section 8.5 Exercises

245.

ⓐ $\frac{4}{3}$ ⓑ $\frac{4}{3}$

247.

ⓐ $\frac{10 m^{2}}{7}$ ⓑ $\frac{3}{y}$

249.

ⓐ $\frac{5}{6 r^{2}}$ ⓑ $\frac{2 x}{3}$

251.

ⓐ $\frac{6 p}{q^{2}}$ ⓑ $- \frac{2 a^{2}}{b}$

253.

ⓐ $\frac{8 m^{4}}{3 n^{4}}$ ⓑ $- \frac{2 x^{2}}{3 y^{2}}$

255.

$2 x^{2} \sqrt{7 y}$

257.

$2 a b \sqrt[3]{2 a}$

259.

ⓐ $\frac{5 \sqrt{6}}{3}$ ⓑ $\frac{2 \sqrt{3}}{9}$ ⓒ $\frac{2 \sqrt{5 x}}{x}$

261.

ⓐ $\frac{6 \sqrt{7}}{7}$ ⓑ $\frac{2 \sqrt{10}}{15}$ ⓒ $\frac{4 \sqrt{3 p}}{p}$

263.

ⓐ $\frac{\sqrt[3]{25}}{5}$ ⓑ $\frac{\sqrt[3]{45}}{6}$ ⓒ $\frac{2 \sqrt[3]{6 a^{2}}}{3 a}$

265.

ⓐ $\frac{\sqrt[3]{121}}{11}$ ⓑ $\frac{\sqrt[3]{28}}{6}$ ⓒ $\frac{\sqrt[3]{9 x}}{x}$

267.

ⓐ $\frac{\sqrt[4]{343}}{7}$ ⓑ $\frac{\sqrt[4]{40}}{4}$ ⓒ $\frac{2 \sqrt[4]{4 x^{2}}}{x}$

269.

ⓐ $\frac{\sqrt[4]{9}}{3}$ ⓑ $\frac{\sqrt[4]{50}}{4}$ ⓒ $\frac{2 \sqrt[4]{3 a^{3}}}{a}$

271.

$−2 (1 + \sqrt{5})$

273.

$3 (3 + \sqrt{7})$

275.

$\frac{\sqrt{3} (\sqrt{m} + \sqrt{5})}{m - 5}$

277.

$\frac{\sqrt{2} (\sqrt{x} + \sqrt{6})}{x - 6}$

279.

${\frac{(\sqrt{r} + \sqrt{5})}{r - 5}}^{2}$

281.

${\frac{(\sqrt{x} + 2 \sqrt{2})}{x - 8}}^{2}$

283.

Answers will vary.

285.

Answers will vary.

Section 8.6 Exercises

287.

$x = 14$

289.

no solution

291.

$x = −4$

293.

$m = 14$

295.

$v = 17$

297.

$m = \frac{7}{2}$

299.

no solution

301.

$u = 3, u = 4$

303.

$r = 1, r = 2$

305.

$x = 10$

307.

$x = −8$

309.

$x = 8$

311.

$x = −4$

313.

$x = 7$

315.

$x = 3$

317.

$z = 21$

319.

$x = 42$

321.

$r = 3$

323.

$u = 3$

325.

$r = −2$

327.

$x = 1$

329.

$x = −8, x = 2$

331.

$a = 0$

333.

$u = \frac{9}{4}$

335.

$a = 4$

337.

$x = 0 x = 4$

339.

$x = 1 x = 5$

341.

$x = 9$

343.

$8.7$ feet

345.

$4.7$ seconds

347.

72 feet

349.

Answers will vary.

Section 8.7 Exercises

351.

ⓐ $f (5) = 4$ ⓑ no value at $x = 0$

353.

ⓐ $g (4) = 5$ ⓑ $g (8) = 7$

355.

ⓐ $F (1) = 1$ ⓑ $F (−11) = 5$

357.

ⓐ $G (5) = 2 \sqrt{6}$ ⓑ $G (2) = 3$

359.

ⓐ $g (6) = 2$ ⓑ $g (−2) = −2$

361.

ⓐ $h (−2) = 0$ ⓑ $h (6) = 2 \sqrt[3]{4}$

363.

ⓐ $f (0) = 0$ ⓑ $f (2) = 2$

365.

ⓐ $g (1) = 0$ ⓑ $g (−3) = 2$

367.

$[\frac{1}{3}, \infty)$

369.

$(− \infty, \frac{2}{3}]$

371.

$(2, \infty)$

373.

$(− \infty, −3] \cup (2, \infty)$

375.

$(− \infty, \infty)$

377.

$(− \infty, \infty)$

379.

$[- \frac{3}{8}, \infty)$

381.

$(− \infty, \infty)$

383.

ⓐ domain: $[−1, \infty)$
ⓑ

$The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 7. The y-axis runs from negative 2 to 10. The function has a starting point at (negative 1, 0) and goes through the points (0, 1) and (3, 2).$

385.

ⓐ domain: $[−4, \infty)$
ⓑ

$The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a starting point at (negative 4, 0) and goes through the points (negative 3, 1) and (0, 2).$

387.

ⓐ domain: $[0, \infty)$
ⓑ

$The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 2) and goes through the points (1, 3) and (4, 4).$

389.

ⓐ domain: $[0, \infty)$
ⓑ

391.

ⓐ domain: $(− \infty, 3]$
ⓑ

$The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 6 to 4. The y-axis runs from 0 to 8. The function has a starting point at (3, 0) and goes through the points (2, 1), (negative 1, 2), and (negative 6, 3).$

393.

ⓐ domain: $[0, \infty)$
ⓑ

$The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from negative 8 to 0. The function has a starting point at (0, 0) and goes through the points (1, negative 1) and (4, negative 2).$

395.

ⓐ domain: $(− \infty, \infty)$
ⓑ

$The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 1, 0) and goes through the points (negative 2, negative 1) and (0, 1).$

397.

ⓐ domain: $(− \infty, \infty)$
ⓑ

$The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 4, 0) and goes through the points (negative 3, negative 1) and (negative 1, 1).$

399.

ⓐ domain: $(− \infty, \infty)$
ⓑ

$The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a center point at (0, 3) and goes through the points (negative 1, 2) and (1, 4).$

401.

ⓐ domain: $(− \infty, \infty)$
ⓑ

$The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 1) and (negative 1, negative 1).$

403.

ⓐ domain: $(− \infty, \infty)$
ⓑ

$The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 2) and (negative 1, negative 2).$

405.

Answers will vary.

407.

Answers will vary.

Section 8.8 Exercises

409.

411.

413.

$9 \sqrt{3} i$

415.

$8 \sqrt{2} i$

417.

$8 + 7 i$

419.

$14 + 2 i$

421.

$−2 + 2 i$

423.

$8 + 5 i$

425.

$7 - 13 i$

427.

$25 - 2 \sqrt{2} i$

429.

$12 + 20 i$

431.

$−12 + 18 i$

433.

$−38 + + 9 i$

435.

$27 + 15 i$

437.

$−7 + 24 i$

439.

$−5 + 12 i$

441.

$−30$

443.

$−30$

445.

$−44 - 4 i \sqrt{3}$

447.

$−20 - 2 \sqrt{2} i$

449.

451.

453.

455.

457.

459.

$\frac{2}{25} + \frac{11}{25} i$

461.

$\frac{6}{13} + \frac{9}{13} i$

463.

$- \frac{12}{13} - \frac{8}{13} i$

465.

$\frac{4}{3} - \frac{1}{3} i$

467.

$- \frac{3}{4} + \frac{1}{2} i$

469.

471.

$−1$

473.

475.

477.

Answers will vary.

479.

Answers will vary.

Review Exercises

481.

ⓐ 15 ⓑ $−4$

483.

ⓐ 2 ⓑ 3 ⓒ 3

485.

ⓐ $8 < \sqrt{68} < 9$
ⓑ $4 < \sqrt[3]{84} < 5$

487.

ⓐ a ⓑ $b$

489.

ⓐ $m^{2}$ ⓑ $n^{4}$

491.

ⓐ $6 a^{2}$ ⓑ $2 b^{4}$

493.

$5 \sqrt{5}$

495.

ⓐ $5 \sqrt[3]{5}$ ⓑ $2 \sqrt[6]{2}$

497.

499.

ⓐ $−2$ ⓑ not real

501.

503.

$\frac{5 m^{2} \sqrt{3 m}}{4}$

505.

507.

509.

ⓐ 5 ⓑ 3 ⓒ 2

511.

513.

515.

517.

519.

521.

$37 y \sqrt{3}$

523.

ⓐ $126 x^{2} \sqrt{x}$ ⓑ $48 a \sqrt[3]{5 a^{2}}$

525.

ⓐ $71 - 22 \sqrt{7}$
ⓑ $\sqrt[3]{x^{2}} - 8 \sqrt[3]{x} + 15$

527.

ⓐ $27 + 8 \sqrt{11}$ ⓑ $29 - 12 \sqrt{5}$

529.

$\sqrt[3]{9 x^{2}} - 4$

531.

ⓐ $\frac{8 m^{4}}{3 n^{4}}$ ⓑ $- \frac{2 x^{2}}{3 y^{2}}$

533.

535.

$- \frac{7 (2 + \sqrt{6})}{2}$

537.

${\frac{(\sqrt{x} + 2 \sqrt{2})}{x - 8}}^{2}$

539.

no solution

541.

$u = 3, u = 4$

543.

$x = −4$

545.

$r = 3$

547.

$x = −8, x = 2$

549.

$x = 3$

551.

$64.8$ feet

553.

ⓐ $G (5) = 2 \sqrt{6}$ ⓑ $G (2) = 3$

555.

ⓐ $g (1) = 0$ ⓑ $g (−3) = 2$

557.

$(2, \infty)$

559.

$(- \infty, \frac{10}{7}]$

561.

ⓐ domain: $[0, \infty)$
ⓑ

563.

ⓐ domain: $(− \infty, \infty)$
ⓑ

565.

$8 \sqrt{2} i$

567.

$8 + 5 i$

569.

$23 + 14 i$

571.

$−8$

573.

$−5 + 12 i$

575.

$\frac{2}{25} + \frac{11}{25} i$

577.

Practice Test

579.

$5 x^{3}$

581.

$2 x^{2} y^{} \sqrt[3]{9 x^{2} y}$

583.

ⓐ $\frac{1}{4}$ ⓑ $−343$

585.

$x^{\frac{7}{4}}$

587.

$− x^{2} \sqrt{3 x}$

589.

$36 x^{4} \sqrt{2}$

591.

$2 - 7 \sqrt{3}$

593.

$\frac{7 x^{2} \sqrt{x} \sqrt{y}}{3 y^{4}}$

595.

$3 (2 - \sqrt{3})$

597.

$−12 + 8 i$

599.

$1$

601.

$x = 4$

603.

ⓐ domain: $[−2, \infty)$
ⓑ

Search

Text Color

Text Size

Margin Size

Font Type

Be Prepared

Try It

Section 8.1 Exercises

Section 8.2 Exercises

Section 8.3 Exercises

Section 8.4 Exercises

Section 8.5 Exercises

Section 8.6 Exercises

Section 8.7 Exercises

Section 8.8 Exercises

Review Exercises

Practice Test