Chapter 8 Algebra Review Pg 522 Answer Geometry

Be Prepared

viii.3

ⓐ ${\mathrm{ten}}^{\mathrm{six}}$ ; ⓑ $y^{\mathrm{half-dozen}}$ ; ⓒ $z^{12}$

8.8

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

viii.10

$\mathrm{two}{x}^2+11x-\mathrm{eight}$

8.11

$8+\mathrm{ii}a-a^{\mathrm{ii}}$

viii.12

$81-90y+25y^2$

8.15

$49-\mathrm{ix}{\mathrm{10}}^{\mathrm{two}}$

8.sixteen

$y^2-6y+9$

8.18

$n=2\text{or}n=4$

8.19

$(\text{−}\infty ,\frac{\mathrm{ane}}{2}]$

8.20

$f(2)=2,f(\mathrm{-1})=\mathrm{-7},f(0)=\mathrm{-four}$

8.21

$\text{domain:}[0,\infty );\text{range:}[0,\infty )$

8.22

ⓐ $\mathrm{-4},0.\bar{5},\frac{7}{\mathrm{three}},3,\sqrt{81};$ ⓑ $\sqrt{\mathrm{seven}};$ ⓒ $\mathrm{-four},-\sqrt{\mathrm{vii}},0.\bar{5},\frac{\mathrm{vii}}{3},\mathrm{iii},\sqrt{81}$

8.23

$2x^2-\mathrm{10}-15$

8.24

$\frac{\sqrt{\mathrm{five}}\left(\sqrt{\mathrm{fifteen}}\right)}{2}$

Endeavor It

8.3

ⓐ not a real number ⓑ $\mathrm{-9}$

8.4

ⓐ $\mathrm{-7}$ ⓑ not a real number

viii.vii

ⓐ $\mathrm{-3}$ ⓑ not real ⓒ $\mathrm{-2}$

8.8

ⓐ $\mathrm{-6}$ ⓑ not real ⓒ $\mathrm{-iv}$

viii.ix

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

8.10

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

8.11

ⓐ $\approx 3.32$ ⓑ $\approx \mathrm{4.xiv}$
ⓒ $\approx \mathrm{iii.36}$

8.12

ⓐ $\approx 3.61$ ⓑ $\approx \mathrm{four.38}$
ⓒ $\approx 3.15$

viii.13

ⓐ $\left|b\right|$ ⓑ westward ⓒ $\left|\mathrm{1000}\right|$ ⓓ q

viii.14

ⓐ $\left|y\right|$ ⓑ p ⓒ $\left|z\right|$ ⓓ q

8.xix

ⓐ $8\left|x\right|$ ⓑ $\mathrm{-x}\left|p\right|$

8.20

ⓐ $13\left|y\right|$ ⓑ $\mathrm{-11}\left|y\right|$

viii.21

ⓐ $\mathrm{three}{x}^9$ ⓑ $3\left|q^{\mathrm{seven}}\right|$

eight.23

ⓐ $10\left|ab\right|$ ⓑ $12p^6{q}^{\mathrm{x}}$
ⓒ $2{\mathrm{ten}}^{10}{y}^4$

eight.24

ⓐ $15\left|mn\right|$ ⓑ $\mathrm{xiii}\left|x^5{y}^7\right|$
ⓒ $\mathrm{three}{\mathrm{westward}}^{12}{z}^5$

8.27

ⓐ $12\sqrt{2}$ ⓑ $3\sqrt[3]{3}$ ⓒ $2\sqrt[\mathrm{iv}]{\mathrm{four}}$

8.28

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

8.29

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

8.30

ⓐ $p^4\sqrt{p}$ ⓑ $y\sqrt[5]{y^3}$
ⓒ $q^{\mathrm{two}}\sqrt[\mathrm{half\; dozen}]{q}$

8.31

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

8.32

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

8.33

ⓐ $\mathrm{vii}\left|a^3\right|b^{\mathrm{ii}}{\sqrt{2ab}}^{}$
ⓑ $\mathrm{two}xy\sqrt[3]{7x^{\mathrm{two}}y}$ ⓒ $2\left|\mathrm{ten}\right|y^{\mathrm{two}}\sqrt[4]{2x}$

8.34

ⓐ $\mathrm{half-dozen}{\mathrm{one\; thousand}}^{\mathrm{four}}\left|{\mathrm{due\; north}}^5\right|\sqrt{\mathrm{five}mn}$
ⓑ $2x^{2}y\sqrt[3]{\mathrm{nine}{y}^2}$ ⓒ $2\left|\mathrm{10}y\right|\sqrt[4]{5x^{\mathrm{three}}}$

eight.35

ⓐ $\mathrm{-4}$ ⓑ $\text{no real number}$

8.36

ⓐ $\mathrm{-5}\sqrt[3]{5}$ ⓑ no real number

8.39

ⓐ $\frac{5}{\mathrm{iv}}$ ⓑ $\frac{3}{\mathrm{five}}$ ⓒ $\frac{2}{\mathrm{three}}$

8.40

ⓐ $\frac{\mathrm{vii}}{9}$ ⓑ $\frac{2}{\mathrm{v}}$ ⓒ $\frac{1}{3}$

8.41

ⓐ $\left|a\right|$ ⓑ $\left|x\right|$ ⓒ $y^3$

8.42

ⓐ $x^{\mathrm{ii}}$ ⓑ $g^{\mathrm{ii}}$ ⓒ $n^{\mathrm{ii}}$

viii.43

$\frac{2\left|p\right|\sqrt{6p}}{\mathrm{vii}}$

8.44

$\frac{2x^2\sqrt{\mathrm{three}\mathrm{10}}}{5}$

eight.45

ⓐ $\frac{\mathrm{four}\left|g\right|\sqrt{5\mathrm{grand}}}{\left|{\mathrm{north}}^3\right|}$ ⓑ $\frac{\mathrm{iii}{c}^{\mathrm{three}}\sqrt[\mathrm{three}]{\mathrm{iv}c}}{d^2}$
ⓒ $\frac{\mathrm{two}{x}^2\sqrt[4]{\mathrm{five}{\mathrm{10}}^2}}{\left|y\right|}$

viii.46

ⓐ $\frac{3u^3\sqrt{6u}}{v^4}$ ⓑ $\frac{\mathrm{two}r\sqrt[3]{5}}{s^2}$
ⓒ $\frac{\mathrm{three}\left|m^3\right|\sqrt[\mathrm{iv}]{2{\mathrm{grand}}^2}}{\left|n^3\right|}$

8.47

ⓐ $\frac{5\left|y\right|\sqrt{x}}{6}$ ⓑ $\frac{\mathrm{ii}xy\sqrt[3]{y^2}}{\mathrm{three}}$
ⓒ $\frac{\left|ab\right|\sqrt[\mathrm{iv}]{a}}{2}$

8.48

ⓐ $\frac{2\left|m\right|\sqrt{3}}{5\left|n^{\mathrm{iii}}\right|}$ ⓑ $\frac{3\mathrm{ten}y\sqrt[3]{{\mathrm{ten}}^2}}{5}$
ⓒ $\frac{2\left|ab\right|\sqrt[\mathrm{four}]{a^{\mathrm{ii}}}}{3}$

8.49

ⓐ $7z^2$ ⓑ $\mathrm{-5}\sqrt[\mathrm{iii}]{2}$
ⓒ $3\left|\mathrm{chiliad}\right|\sqrt[\mathrm{four}]{2m^2}$

viii.50

ⓐ $\mathrm{eight}{m}^4$ ⓑ $\mathrm{-4}$ ⓒ $3\left|n\right|\sqrt[\mathrm{iv}]{2}$

viii.52

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

8.53

ⓐ ${(\mathrm{ten}m)}^{\frac{1}{\mathrm{two}}}$ ⓑ ${(3\mathrm{north})}^{\frac{1}{5}}$
ⓒ $3{(\mathrm{six}y)}^{\frac{1}{\mathrm{four}}}$

eight.54

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

8.57

ⓐ No existent solution ⓑ $\mathrm{-eight}$
ⓒ $\frac{1}{8}$

eight.58

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

8.59

ⓐ ${\mathrm{ten}}^{\frac{5}{2}}$ ⓑ ${\left(3y\right)}^{\frac{\mathrm{three}}{\mathrm{iv}}}$ ⓒ ${\left(\frac{2\mathrm{one\; thousand}}{\mathrm{iii}\mathrm{northward}}\right)}^{\frac{5}{2}}$

8.60

ⓐ $a^{\frac{\mathrm{two}}{5}}$ ⓑ ${\left(\mathrm{five}ab\right)}^{\frac{5}{\mathrm{iii}}}$
ⓒ ${\left(\frac{7xy}{z}\right)}^{\frac{\mathrm{iii}}{\mathrm{ii}}}$

8.61

ⓐ 9 ⓑ $\frac{\mathrm{ane}}{729}$ ⓒ $\frac{1}{8}$

eight.62

ⓐ 8 ⓑ $\frac{\mathrm{i}}{9}$ ⓒ $\frac{1}{125}$

8.63

ⓐ $\mathrm{-64}$ ⓑ $-\frac{1}{64}$ ⓒ not a existent number

8.64

ⓐ $\mathrm{-729}$ ⓑ $-\frac{\mathrm{i}}{729}$ ⓒ non a real number

8.65

ⓐ $x^{\frac{3}{2}}$ ⓑ $x^{\mathrm{viii}}$ ⓒ $\frac{\mathrm{i}}{x}$

8.66

ⓐ $y^{\frac{11}{8}}$ ⓑ ${\mathrm{chiliad}}^2$ ⓒ $\frac{\mathrm{ane}}{d}$

8.67

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

eight.68

ⓐ $729n^{\frac{3}{5}}$ ⓑ $a^{\mathrm{ii}}{b}^{\frac{\mathrm{two}}{3}}$

8.70

ⓐ $u^3$ ⓑ $3x^{\frac{\mathrm{ane}}{\mathrm{v}}}{y}^{\frac{\mathrm{ane}}{\mathrm{iii}}}$

8.71

ⓐ $\text{−}\sqrt{2}$ ⓑ $\mathrm{eleven}\sqrt[3]{x}$
ⓒ $3\sqrt[4]{\mathrm{10}}-5\sqrt[\mathrm{iv}]{y}$

8.72

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

8.73

ⓐ $\mathrm{-two}\sqrt{7x}$ ⓑ $\text{−}\sqrt[4]{5xy}$

8.74

ⓐ $\text{−}\sqrt{3y}$ ⓑ $\mathrm{three}\sqrt[3]{\mathrm{seven}mn}$

8.75

ⓐ $\mathrm{nine}\sqrt{2}$ ⓑ $2\sqrt[\mathrm{three}]{2}$ ⓒ $\sqrt[3]{3}$

8.76

ⓐ $7\sqrt{\mathrm{three}}$ ⓑ $\mathrm{-10}\sqrt[3]{5}$ ⓒ $\mathrm{-three}\sqrt[\mathrm{iii}]{\mathrm{two}}$

eight.77

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

8.78

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

8.79

ⓐ $12\sqrt{15}$ ⓑ $\mathrm{-18}\sqrt[3]{\mathrm{iv}}$

8.lxxx

ⓐ $27\sqrt{2}$ ⓑ $\mathrm{-36}\sqrt[\mathrm{three}]{2}$

8.81

ⓐ $288{\mathrm{10}}^3\sqrt{\mathrm{five}}$ ⓑ $8y\sqrt[4]{6y^2}$

8.82

ⓐ $144y^{\mathrm{ii}}\sqrt{5y}$ ⓑ $\mathrm{-36}a\sqrt[4]{3a}$

8.83

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

8.84

ⓐ $\mathrm{-twoscore}+4\sqrt{2}$ ⓑ $\mathrm{-iii}-\sqrt[3]{18}$

8.85

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

8.86

ⓐ $41-\mathrm{fourteen}\sqrt{11}$
ⓑ $\sqrt[3]{{\mathrm{10}}^2}+\mathrm{four}\sqrt[3]{\mathrm{10}}+\mathrm{iii}$

8.88

$\mathrm{-12}-20\sqrt{\mathrm{iii}}$

8.89

ⓐ $102+20\sqrt{2}$ ⓑ $55+6\sqrt{\mathrm{half\; dozen}}$

viii.90

ⓐ $41-12\sqrt{5}$
ⓑ $121-36\sqrt{10}$

8.95

ⓐ $\frac{\mathrm{nine}{\mathrm{ten}}^2}{y^2}$ ⓑ $\frac{\mathrm{-4}\mathrm{ten}}{y}$

8.96

ⓐ $\frac{10{\mathrm{north}}^3}{\mathrm{thousand}}$ ⓑ $\frac{\mathrm{-three}p}{q^2}$

8.99

ⓐ $\frac{5\sqrt{3}}{3}$ ⓑ $\frac{\sqrt{\mathrm{vi}}}{\mathrm{viii}}$ ⓒ $\frac{\sqrt{\mathrm{two}x}}{x}$

8.100

ⓐ $\frac{\mathrm{half-dozen}\sqrt{5}}{5}$ ⓑ $\frac{\sqrt{\mathrm{xiv}}}{6}$ ⓒ $\frac{\sqrt{5x}}{x}$

8.101

ⓐ $\frac{\sqrt[3]{49}}{7}$ ⓑ $\frac{\sqrt[\mathrm{three}]{\mathrm{ninety}}}{6}$ ⓒ $\frac{\mathrm{five}\sqrt[3]{\mathrm{iii}{y}^2}}{\mathrm{three}y}$

8.102

ⓐ $\frac{\sqrt[3]{\mathrm{iv}}}{\mathrm{ii}}$ ⓑ $\frac{\sqrt[3]{150}}{\mathrm{ten}}$ ⓒ $\frac{\mathrm{ii}\sqrt[3]{5{\mathrm{north}}^2}}{\mathrm{v}\mathrm{northward}}$

8.103

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

viii.104

ⓐ $\frac{\sqrt[4]{125}}{5}$ ⓑ $\frac{\sqrt[4]{\mathrm{fourteen}}}{\mathrm{iv}}$
ⓒ $\frac{2\sqrt[\mathrm{four}]{4x^3}}{x}$

viii.105

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

8.107

$\frac{\sqrt{\mathrm{five}}\left(\sqrt{x}-\sqrt{2}\right)}{x-2}$

8.108

$\frac{\sqrt{\mathrm{ten}}\left(\sqrt{y}+\sqrt{\mathrm{iii}}\right)}{y-3}$

8.109

${\frac{\left(\sqrt{p}+\sqrt{\mathrm{ii}}\right)}{p-2}}^{\mathrm{ii}}$

viii.110

${\frac{\left(\sqrt{q}-\sqrt{10}\right)}{q-10}}^{\mathrm{ii}}$

8.113

$\text{no solution}$

eight.114

$\text{no solution}$

8.115

$x=2,\mathrm{10}=3$

8.116

$y=\mathrm{five},y=\mathrm{six}$

8.126

$\mathrm{ten}=-\frac{6}{5}$

8.130

$x=0x=4$

8.135

ⓐ $f\left(6\right)=4$ ⓑ no value at $x=0$

eight.136

ⓐ $g\left(4\right)=\mathrm{five}$ ⓑ no value at $f(\mathrm{-3})$

8.137

ⓐ $\mathrm{one\; thousand}(4)=2$ ⓑ $\mathrm{yard}(1)=\mathrm{-1}$

8.138

ⓐ $h(2)=2$
ⓑ $h(\mathrm{-v})=\mathrm{-3}$

eight.139

ⓐ $f(4)=\mathrm{two}$ ⓑ $f(\mathrm{-1})=1$

eight.140

ⓐ $g(16)=3$ ⓑ $\mathrm{yard}(\mathrm{three})=\mathrm{two}$

viii.141

$\left[\frac{\mathrm{five}}{6},\infty \right)$

8.142

$\left(\text{−}\infty ,\frac{4}{5}\right]$

8.143

$\left(\mathrm{-3},\infty \right)$

8.144

$\left(\mathrm{v},\infty \right)$

viii.145

$(\text{−}\infty ,\infty )$

eight.146

$(\text{−}\infty ,\infty )$

eight.147

ⓐ domain: $\left[\mathrm{-2},\infty \right)$
ⓑ

ⓒ range: $\left[0,\infty \right)$

viii.148

ⓐ domain: $\left[2,\infty \right)$
ⓑ

ⓒ range: $\left[0,\infty \right)$

8.149

ⓐ domain: $\text{(}-\infty ,\infty )$
ⓑ

ⓒ range: $\text{(}-\infty ,\infty )$

8.150

ⓐ domain: $\text{(}-\infty ,\infty )$
ⓑ

ⓒ range: $\text{(}-\infty ,\infty )$

8.151

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

8.152

ⓐ $\mathrm{half-dozen}i$ ⓑ $\sqrt{3}i$ ⓒ $3\sqrt{3}i$

viii.155

ⓐ $6+5i$ ⓑ $6-3i$

8.156

ⓐ $\mathrm{-two}-6i$ ⓑ $\mathrm{two}+9i$

8.157

$12+20i$

viii.159

$\mathrm{-11}-\mathrm{vii}i$

8.160

$\mathrm{-5}-\mathrm{x}i$

viii.161

$\mathrm{-21}-20i$

8.165

$\mathrm{-12}-22\sqrt{\mathrm{iii}}i$

viii.166

$\mathrm{six}+12\sqrt{2}i$

8.173

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

viii.174

$\frac{\mathrm{two}}{5}+\frac{4}{5}i$

8.175

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

8.176

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

Section 8.ane Exercises

7.

ⓐ not real number ⓑ $\mathrm{-17}$

9.

ⓐ $\mathrm{-xv}$ ⓑ non real number

fifteen.

ⓐ $\mathrm{-ii}$ ⓑ $\text{not real}$ ⓒ $\mathrm{-2}$

17.

ⓐ $\mathrm{-5}$ ⓑ $\text{not existent}$ ⓒ $\mathrm{-4}$

19.

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

21.

ⓐ $\mathrm{xiv}<\sqrt{200}<15$
ⓑ $\mathrm{five}<\sqrt[3]{137}<6$

23.

ⓐ $\approx 4.36$ ⓑ $\approx \mathrm{iv.46}$
ⓒ $\approx 3.14$

25.

ⓐ $\approx \mathrm{vii.28}$ ⓑ $\approx 5.28$
ⓒ $\approx 4.61$

33.

ⓐ $x^{12}$ ⓑ $\left|y^{11}\right|$

39.

ⓐ $7\left|x\right|$ ⓑ $\mathrm{-ix}\left|{\mathrm{ten}}^9\right|$

41.

ⓐ $11m^{10}$ ⓑ $\mathrm{-8}\left|a\right|$

47.

ⓐ $12\left|\mathrm{ten}y\right|$ ⓑ $\mathrm{thirteen}{\mathrm{westward}}^4\left|y^5\right|$
ⓒ $\mathrm{two}{a}^{17}{b}^2$

49.

ⓐ $\mathrm{xi}\left|ab\right|$ ⓑ $\mathrm{iii}{c}^{\mathrm{four}}{d}^6$
ⓒ $4x^5{y}^{22}$

Section 8.ii Exercises

67.

ⓐ $\left|y^5\right|\sqrt[]{y}$ ⓑ $r\sqrt[3]{r^{\mathrm{ii}}}$ ⓒ ${\mathrm{south}}^2\sqrt[\mathrm{four}]{s^2}$

69.

ⓐ $n^{10}\sqrt{n}$ ⓑ $q^2\sqrt[3]{q^2}$
ⓒ $\left|n\right|\sqrt[8]{{\mathrm{due\; north}}^{\mathrm{ii}}}$

71.

ⓐ $5r^6\sqrt[]{\mathrm{v}r}$ ⓑ $3x\sqrt[\mathrm{iii}]{4x^2}$
ⓒ $2\left|y\right|\sqrt[4]{\mathrm{iii}{y}^{\mathrm{two}}}$

73.

ⓐ $11\left|m^{11}\right|\sqrt[]{\mathrm{two}m}$ ⓑ $3g^{\mathrm{two}}\sqrt[4]{5m^{\mathrm{ii}}}$ ⓒ $2n\sqrt[\mathrm{five}]{5n^{\mathrm{three}}}$

75.

ⓐ $\mathrm{vii}\left|m^{\mathrm{iii}}{n}^5\right|\sqrt[]{\mathrm{three}mn}$ ⓑ $2{\mathrm{ten}}^2{y}^{\mathrm{two}}\sqrt[3]{\mathrm{vi}y}$ ⓒ $\mathrm{ii}\left|xy\right|\sqrt[\mathrm{four}]{2x}$

77.

ⓐ $8\left|q{r}^3\right|\sqrt{\mathrm{three}qr}$ ⓑ $\mathrm{three}{m}^{\mathrm{three}}{\mathrm{due\; north}}^3\sqrt[\mathrm{three}]{2n}$ ⓒ $3a^{\mathrm{ii}}{b}^{\mathrm{ii}}\sqrt[\mathrm{four}]{a}$

79.

ⓐ $\mathrm{-6}\sqrt[\mathrm{three}]{4}$ ⓑ not real

85.

ⓐ $\mathrm{one}+3\sqrt{\mathrm{v}}$ ⓑ $1+\sqrt{10}$

91.

ⓐ ${\mathrm{10}}^2$ ⓑ $p^3$ ⓒ $\left|q\right|$

93.

ⓐ $\frac{1}{y^{\mathrm{two}}}$ ⓑ $u^2$ ⓒ $\left|v^{\mathrm{three}}\right|$

95.

$\frac{4\left|x^3\right|\sqrt{6\mathrm{ten}}}{\mathrm{eleven}}$

97.

$\frac{5g^{\mathrm{ii}}\sqrt{3\mathrm{yard}}}{\mathrm{four}}$

99.

$\frac{\mathrm{vii}{r}^{\mathrm{ii}}\sqrt{2r}}{10}$

101.

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

103.

ⓐ $\frac{5r^4\sqrt{3r}}{s^4}$ ⓑ $\frac{\mathrm{three}{a}^{\mathrm{two}}\sqrt[3]{2a^2}}{b}$
ⓒ $\frac{2\left|c\right|\sqrt[\mathrm{four}]{\mathrm{iv}c}}{\left|d\right|}$

105.

ⓐ $\frac{\mathrm{ii}\left|p^{\mathrm{iii}}\right|\sqrt{\mathrm{seven}p}}{\left|q\right|}$ ⓑ $\frac{3s^2\sqrt[\mathrm{iii}]{3{\mathrm{southward}}^2}}{t}$
ⓒ $\frac{\mathrm{two}\left|p^{\mathrm{three}}\right|\sqrt[4]{4p^3}}{\left|q^3\right|}$

107.

ⓐ $\frac{\mathrm{iv}\left|xy\right|}{3}$ ⓑ $\frac{y^{\mathrm{two}}\sqrt[3]{\mathrm{ten}}}{\mathrm{ii}}$ ⓒ $\frac{\left|ab\right|\sqrt[4]{a}}{2}$

109.

ⓐ $\frac{1}{2\left|pq\right|}$ ⓑ $\frac{\mathrm{two}cd\sqrt[\mathrm{three}]{d^2}}{5}$
ⓒ $\frac{\left|\mathrm{thousand}n\right|}{2}$

111.

ⓐ $\frac{\mathrm{three}{p}^{\mathrm{four}}\sqrt{p}}{\left|q\right|}$ ⓑ $2\sqrt[\mathrm{four}]{2}$
ⓒ $2\mathrm{ten}\sqrt[5]{2x}$

113.

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

Section 8.3 Exercises

121.

ⓐ $\sqrt[5]{u}$ ⓑ $\sqrt[9]{5}$ ⓒ $\sqrt[20]{\mathrm{west}}$

123.

ⓐ ${\mathrm{10}}^{\frac{1}{7}}$ ⓑ $y^{\frac{1}{9}}$ ⓒ $f^{\frac{\mathrm{i}}{\mathrm{v}}}$

125.

ⓐ ${\left(7c\right)}^{\frac{1}{\mathrm{three}}}$ ⓑ ${\left(12d\right)}^{\frac{1}{\mathrm{vii}}}$
ⓒ $2{\left(6b\right)}^{\frac{1}{4}}$

127.

ⓐ ${\left(21p\right)}^{\frac{1}{2}}$ ⓑ ${\left(\mathrm{viii}q\right)}^{\frac{1}{4}}$
ⓒ $4{\left(36r\right)}^{\frac{1}{\mathrm{half\; dozen}}}$

133.

ⓐ $\mathrm{-half-dozen}$ ⓑ $\mathrm{-6}$ ⓒ $\frac{1}{6}$

135.

ⓐ not real ⓑ $\mathrm{-iii}$ ⓒ $\frac{1}{3}$

137.

ⓐ not existent ⓑ $\mathrm{-6}$ ⓒ $\frac{1}{6}$

139.

ⓐ not existent ⓑ $\mathrm{-10}$ ⓒ $\frac{1}{\mathrm{ten}}$

141.

ⓐ $m^{\frac{5}{2}}$ ⓑ ${\left(\mathrm{iii}y\right)}^{\frac{7}{3}}$ ⓒ ${\left(\frac{4x}{\mathrm{five}y}\right)}^{\frac{3}{5}}$

143.

ⓐ $u^{\frac{2}{\mathrm{five}}}$ ⓑ ${\left(6x\right)}^{\frac{5}{3}}$ ⓒ ${\left(\frac{\mathrm{eighteen}a}{\mathrm{v}b}\right)}^{\frac{7}{\mathrm{four}}}$

145.

ⓐ 32,768 ⓑ $\frac{\mathrm{one}}{729}$ ⓒ 9

147.

ⓐ four ⓑ $\frac{1}{\mathrm{nine}}$ ⓒ not real

149.

ⓐ $\mathrm{-27}$ ⓑ $-\frac{1}{27}$ ⓒ non existent

151.

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

153.

ⓐ $y^{\frac{\mathrm{v}}{4}}$ ⓑ $x^8$ ⓒ $\frac{\mathrm{ane}}{\mathrm{one\; thousand}}$

155.

ⓐ $81q^2$ ⓑ $a^{\frac{\mathrm{one}}{2}}b$

157.

ⓐ $\mathrm{eight}{u}^{\frac{\mathrm{one}}{4}}$ ⓑ $8p^{\frac{\mathrm{ane}}{2}}{q}^{\frac{3}{\mathrm{four}}}$

Department 8.4 Exercises

165.

ⓐ $3\sqrt{\mathrm{ii}}$ ⓑ $\mathrm{seven}\sqrt[\mathrm{three}]{m}$ ⓒ $6\sqrt[4]{m}$

167.

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

173.

ⓐ $\mathrm{-2}\sqrt{3}$ ⓑ $\mathrm{-2}\sqrt[\mathrm{iii}]{\mathrm{five}}$ ⓒ $3\sqrt[4]{2}$

175.

ⓐ $\mathrm{vii}\sqrt{3}$ ⓑ $\mathrm{vii}\sqrt[\mathrm{three}]{\mathrm{ii}}$ ⓒ $3\sqrt[4]{5}$

179.

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

183.

ⓐ $\mathrm{-18}\sqrt{6}$ ⓑ $\mathrm{-64}\sqrt[3]{\mathrm{nine}}$

187.

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

189.

ⓐ $\mathrm{-42}{z}^5\sqrt{\mathrm{ii}z}$ ⓑ $\mathrm{-8}y\sqrt[4]{\mathrm{half\; dozen}y}$

191.

ⓐ $\mathrm{fourteen}+\mathrm{five}\sqrt{7}$ ⓑ $\mathrm{four}\sqrt[3]{\mathrm{vi}}+\mathrm{iii}\sqrt[\mathrm{iii}]{\mathrm{iv}}$

193.

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

197.

ⓐ $30+18\sqrt{\mathrm{ii}}$ ⓑ $\sqrt[\mathrm{iii}]{{\mathrm{10}}^{\mathrm{ii}}}-2\sqrt[3]{x}-\mathrm{iii}$

199.

ⓐ $\mathrm{-55}+13\sqrt{10}$
ⓑ $2\sqrt[\mathrm{iii}]{x^{\mathrm{two}}}+8\sqrt[3]{x}+6$

203.

$\mathrm{-439}-2\sqrt{77}$

205.

ⓐ $14+\mathrm{vi}\sqrt{5}$ ⓑ $79-\mathrm{xx}\sqrt{3}$

207.

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

215.

$\sqrt[3]{\mathrm{ix}{\mathrm{ten}}^2}-\mathrm{four}$

223.

$10c^2\sqrt{3}-\mathrm{nine}{c}^3\sqrt{3}$

Section viii.5 Exercises

251.

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

253.

ⓐ $\frac{\mathrm{eight}{\mathrm{grand}}^4}{\mathrm{iii}{n}^4}$ ⓑ $-\frac{2x^{\mathrm{ii}}}{3y^2}$

257.

$\mathrm{two}ab\sqrt[3]{2a}$

259.

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

261.

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

263.

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

265.

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

267.

ⓐ $\frac{\sqrt[4]{343}}{\mathrm{vii}}$ ⓑ $\frac{\sqrt[\mathrm{iv}]{\mathrm{forty}}}{\mathrm{four}}$ ⓒ $\frac{2\sqrt[4]{\mathrm{four}{\mathrm{ten}}^2}}{x}$

269.

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

271.

$\mathrm{-two}\left(\mathrm{i}+\sqrt{5}\right)$

273.

$\mathrm{iii}\left(\mathrm{iii}+\sqrt{7}\right)$

275.

$\frac{\sqrt{3}\left(\sqrt{m}+\sqrt{5}\right)}{\mathrm{thousand}-\mathrm{five}}$

277.

$\frac{\sqrt{\mathrm{ii}}\left(\sqrt{x}+\sqrt{6}\right)}{x-6}$

279.

${\frac{\left(\sqrt{r}+\sqrt{\mathrm{five}}\right)}{r-\mathrm{v}}}^{\mathrm{ii}}$

281.

${\frac{\left(\sqrt{\mathrm{ten}}+2\sqrt{2}\right)}{x-\mathrm{eight}}}^2$

Section 8.vi Exercises

301.

$u=\mathrm{iii},u=\mathrm{iv}$

303.

$r=\mathrm{one},r=\mathrm{ii}$

329.

$\mathrm{10}=\mathrm{-8},x=\mathrm{ii}$

337.

$x=0x=4$

339.

$x=1x=5$

Section viii.7 Exercises

351.

ⓐ $f(5)=4$ ⓑ no value at $\mathrm{ten}=0$

353.

ⓐ $g(\mathrm{iv})=5$ ⓑ $\mathrm{thousand}(8)=\mathrm{seven}$

355.

ⓐ $F(\mathrm{one})=1$ ⓑ $F(\mathrm{-11})=\mathrm{five}$

357.

ⓐ $G(5)=2\sqrt{\mathrm{six}}$ ⓑ $\mathrm{Yard}(\mathrm{two})=3$

359.

ⓐ $m(6)=\mathrm{two}$ ⓑ $g(\mathrm{-2})=\mathrm{-2}$

361.

ⓐ $h(\mathrm{-ii})=0$ ⓑ $h(6)=\mathrm{ii}\sqrt[3]{4}$

363.

ⓐ $f(0)=0$ ⓑ $f(\mathrm{ii})=2$

365.

ⓐ $g(1)=0$ ⓑ $\mathrm{thousand}(\mathrm{-3})=\mathrm{ii}$

367.

$\left[\frac{1}{\mathrm{iii}},\infty \right)$

369.

$\left(\text{−}\infty ,\frac{\mathrm{two}}{3}\right]$

373.

$\left(\text{−}\infty ,\mathrm{-3}\right]\cup \left(2,\infty \right)$

375.

$\left(\text{−}\infty ,\infty \right)$

377.

$\left(\text{−}\infty ,\infty \right)$

379.

$\left[-\frac{\mathrm{three}}{8},\infty \right)$

381.

$\left(\text{−}\infty ,\infty \right)$

383.

ⓐ domain: $\left[\mathrm{-i},\infty \right)$
ⓑ

ⓒ $\left[0,\infty \right)$

385.

ⓐ domain: $\left[\mathrm{-iv},\infty \right)$
ⓑ

ⓒ $\left[0,\infty \right)$

387.

ⓐ domain: $\left[0,\infty \right)$
ⓑ

ⓒ $\left[2,\infty \right)$

389.

ⓐ domain: $\left[0,\infty \right)$
ⓑ

ⓒ $\left[0,\infty \right)$

391.

ⓐ domain: $\left(\text{−}\infty ,3\right]$
ⓑ

ⓒ $\left[0,\infty \right)$

393.

ⓐ domain: $\left[0,\infty \right)$
ⓑ

ⓒ $\left(\text{−}\infty ,0\right]$

395.

ⓐ domain: $\left(\text{−}\infty ,\infty \right)$
ⓑ

ⓒ $\left(\text{−}\infty ,\infty \right)$

397.

ⓐ domain: $\left(\text{−}\infty ,\infty \right)$
ⓑ

ⓒ $\left(\text{−}\infty ,\infty \right)$

399.

ⓐ domain: $\left(\text{−}\infty ,\infty \right)$
ⓑ

ⓒ $\left(\text{−}\infty ,\infty \right)$

401.

ⓐ domain: $\left(\text{−}\infty ,\infty \right)$
ⓑ

ⓒ $\left(\text{−}\infty ,\infty \right)$

403.

ⓐ domain: $\left(\text{−}\infty ,\infty \right)$
ⓑ

ⓒ $\left(\text{−}\infty ,\infty \right)$

Department 8.8 Exercises

409.

ⓐ $\mathrm{four}i$ ⓑ $\sqrt{\mathrm{xi}}i$ ⓒ $\mathrm{ii}\sqrt{\mathrm{ii}}i$

411.

ⓐ $10i$ ⓑ $\sqrt{13}i$ ⓒ $\mathrm{three}\sqrt{5}i$

427.

$25-2\sqrt{2}i$

431.

$\mathrm{-12}+18i$

433.

$\mathrm{-38}++9i$

445.

$\mathrm{-44}-\mathrm{iv}i\sqrt{3}$

447.

$\mathrm{-20}-\mathrm{ii}\sqrt{2}i$

459.

$\frac{\mathrm{ii}}{25}+\frac{11}{25}i$

461.

$\frac{\mathrm{half\; dozen}}{13}+\frac{\mathrm{ix}}{\mathrm{thirteen}}i$

463.

$-\frac{12}{13}-\frac{\mathrm{eight}}{13}i$

465.

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

467.

$-\frac{\mathrm{three}}{\mathrm{iv}}+\frac{1}{2}i$

Review Exercises

485.

ⓐ $\mathrm{viii}<\sqrt{68}<9$
ⓑ $4<\sqrt[\mathrm{three}]{84}<5$

497.

ⓐ $4\left|s^{\mathrm{seven}}\right|\sqrt[]{5s}$ ⓑ $\mathrm{two}a\sqrt[5]{3a^2}$
ⓒ $\mathrm{two}\left|b\right|\sqrt[6]{\mathrm{two}b}$

501.

ⓐ $\frac{6}{7}$ ⓑ $\frac{2}{\mathrm{three}}$ ⓒ $\frac{\mathrm{i}}{2}$

503.

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

505.

ⓐ $\frac{1}{\mathrm{two}\left|pq\right|}$ ⓑ $\frac{2cd\sqrt[5]{2d^2}}{5}$
ⓒ $\frac{\left|mn\right|}{\mathrm{ii}}$

511.

ⓐ $\mathrm{-two}$ ⓑ $\frac{\mathrm{i}}{3}$ ⓒ $\mathrm{-5}$

515.

ⓐ ${\mathrm{half-dozen}}^3$ ⓑ $b^9$ ⓒ $\frac{\mathrm{one}}{w}$

517.

ⓐ $4\sqrt{2}$ ⓑ $\mathrm{ix}\sqrt[3]{p}$ ⓒ $2\sqrt[\mathrm{iii}]{x}$

519.

ⓐ $7\sqrt{3}$ ⓑ $7\sqrt[3]{2}$ ⓒ $\mathrm{iii}\sqrt[4]{\mathrm{five}}$

523.

ⓐ $126{\mathrm{10}}^2\sqrt{x}$ ⓑ $48a\sqrt[3]{5a^2}$

525.

ⓐ $71-22\sqrt{\mathrm{vii}}$
ⓑ $\sqrt[3]{x^2}-8\sqrt[3]{\mathrm{ten}}+\mathrm{fifteen}$

527.

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

529.

$\sqrt[3]{9{\mathrm{10}}^2}-4$

531.

ⓐ $\frac{\mathrm{viii}{m}^4}{3n^4}$ ⓑ $-\frac{2{\mathrm{10}}^{\mathrm{ii}}}{\mathrm{three}{y}^2}$

533.

ⓐ $\frac{\sqrt[\mathrm{iii}]{121}}{\mathrm{eleven}}$ ⓑ $\frac{\sqrt[3]{28}}{\mathrm{six}}$ ⓒ $\frac{\sqrt[\mathrm{iii}]{\mathrm{nine}x}}{\mathrm{ten}}$

535.

$-\frac{\mathrm{vii}\left(\mathrm{two}+\sqrt{6}\right)}{\mathrm{ii}}$

537.

${\frac{\left(\sqrt{\mathrm{10}}+2\sqrt{\mathrm{ii}}\right)}{x-8}}^2$

541.

$u=3,u=4$

547.

$x=\mathrm{-8},x=\mathrm{ii}$

553.

ⓐ $G(5)=\mathrm{two}\sqrt{\mathrm{half-dozen}}$ ⓑ $\mathrm{Chiliad}(2)=\mathrm{iii}$

555.

ⓐ $\mathrm{1000}(1)=0$ ⓑ $\mathrm{thou}(\mathrm{-3})=\mathrm{ii}$

559.

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

561.

ⓐ domain: $\left[0,\infty \right)$
ⓑ

ⓒ range: $\left[0,\infty \right)$

563.

ⓐ domain: $\left(\text{−}\infty ,\infty \right)$
ⓑ

ⓒ range: $\left(\text{−}\infty ,\infty \right)$

575.

$\frac{2}{25}+\frac{\mathrm{xi}}{25}i$

Practice Exam

581.

$2{\mathrm{10}}^2{y}^{}\sqrt[3]{9x^{2}y}$

593.

$\frac{7x^2\sqrt{\mathrm{ten}}\sqrt{y}}{\mathrm{three}{y}^4}$

595.

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

603.

ⓐ domain: $\left[\mathrm{-2},\infty \right)$
ⓑ

ⓒ range: $\left[0,\infty \right)$

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Source: https://openstax.org/books/intermediate-algebra-2e/pages/chapter-8

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