Chapter 8 Test Algebra 1

Attempt Information technology

8.3

ⓐ non a real number ⓑ $\mathrm{-nine}$

8.4

ⓐ $\mathrm{-7}$ ⓑ non a real number

8.7

ⓐ $\mathrm{-3}$ ⓑ non existent ⓒ $\mathrm{-2}$

8.eight

ⓐ $\mathrm{-6}$ ⓑ not real ⓒ $\mathrm{-4}$

8.9

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

viii.ten

ⓐ $\mathrm{nine}<\sqrt{84}<10$
ⓑ $5<\sqrt[\mathrm{three}]{152}<\mathrm{half-dozen}$

eight.11

ⓐ $\approx 3.32$ ⓑ $\approx \mathrm{4.xiv}$
ⓒ $\approx 3.36$

8.12

ⓐ $\approx \mathrm{three.61}$ ⓑ $\approx 4.38$
ⓒ $\approx \mathrm{3.xv}$

viii.13

ⓐ $\left|b\right|$ ⓑ w ⓒ $\left|m\right|$ ⓓ q

8.xiv

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

8.nineteen

ⓐ $\mathrm{eight}\left|x\right|$ ⓑ $\mathrm{-10}\left|p\right|$

viii.20

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

8.21

ⓐ $3{\mathrm{ten}}^9$ ⓑ $3\left|q^7\right|$

8.23

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

8.24

ⓐ $15\left|\mathrm{one\; thousand}n\right|$ ⓑ $\mathrm{thirteen}\left|{\mathrm{10}}^{\mathrm{five}}{y}^7\right|$
ⓒ $3{\mathrm{west}}^{12}{z}^5$

8.27

ⓐ $12\sqrt{\mathrm{ii}}$ ⓑ $3\sqrt[3]{3}$ ⓒ $\mathrm{ii}\sqrt[\mathrm{four}]{4}$

eight.28

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

eight.29

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

8.30

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

8.31

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

8.32

ⓐ $\mathrm{v}{a}^4\sqrt{3a}$ ⓑ $4m^3\sqrt[3]{2{\mathrm{thousand}}^2}$
ⓒ $3\left|n\right|\sqrt[4]{2{\mathrm{due\; north}}^{\mathrm{three}}}$

8.33

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

viii.34

ⓐ $\mathrm{half\; dozen}{m}^4\left|n^5\right|\sqrt{5mn}$
ⓑ $2x^{2}y\sqrt[3]{\mathrm{ix}{y}^2}$ ⓒ $2\left|xy\right|\sqrt[4]{\mathrm{five}{\mathrm{10}}^{\mathrm{three}}}$

8.35

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

viii.36

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

8.39

ⓐ $\frac{\mathrm{v}}{4}$ ⓑ $\frac{3}{5}$ ⓒ $\frac{\mathrm{two}}{3}$

viii.40

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

8.41

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

8.42

ⓐ $x^2$ ⓑ $m^2$ ⓒ ${\mathrm{northward}}^2$

8.43

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

8.44

$\frac{2x^2\sqrt{\mathrm{iii}\mathrm{10}}}{\mathrm{five}}$

eight.45

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

8.46

ⓐ $\frac{3u^3\sqrt{6u}}{5^4}$ ⓑ $\frac{\mathrm{ii}r\sqrt[3]{5}}{s^2}$
ⓒ $\frac{3\left|{\mathrm{1000}}^{\mathrm{three}}\right|\sqrt[4]{2m^2}}{\left|n^{\mathrm{three}}\right|}$

8.47

ⓐ $\frac{5\left|y\right|\sqrt{x}}{6}$ ⓑ $\frac{2xy\sqrt[\mathrm{iii}]{y^2}}{3}$
ⓒ $\frac{\left|ab\right|\sqrt[4]{a}}{2}$

8.48

ⓐ $\frac{2\left|m\right|\sqrt{\mathrm{iii}}}{5\left|n^{\mathrm{three}}\right|}$ ⓑ $\frac{3\mathrm{ten}y\sqrt[3]{x^2}}{\mathrm{five}}$
ⓒ $\frac{2\left|ab\right|\sqrt[4]{a^2}}{3}$

8.49

ⓐ $7z^{\mathrm{ii}}$ ⓑ $\mathrm{-v}\sqrt[3]{2}$
ⓒ $3\left|m\right|\sqrt[4]{\mathrm{two}{m}^2}$

8.fifty

ⓐ $8m^4$ ⓑ $\mathrm{-4}$ ⓒ $3\left|n\right|\sqrt[4]{\mathrm{ii}}$

8.52

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

8.53

ⓐ ${(10m)}^{\frac{\mathrm{ane}}{2}}$ ⓑ ${(3\mathrm{due\; north})}^{\frac{1}{5}}$
ⓒ $\mathrm{iii}{(6y)}^{\frac{\mathrm{one}}{4}}$

8.54

ⓐ ${(\mathrm{three}k)}^{\frac{1}{7}}$ ⓑ ${(\mathrm{five}j)}^{\frac{\mathrm{one}}{4}}$
ⓒ $8{(\mathrm{two}a)}^{\frac{1}{\mathrm{iii}}}$

8.57

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

eight.58

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

8.59

ⓐ ${\mathrm{ten}}^{\frac{5}{2}}$ ⓑ ${\left(3y\right)}^{\frac{3}{4}}$ ⓒ ${\left(\frac{\mathrm{two}g}{\mathrm{iii}n}\right)}^{\frac{\mathrm{five}}{2}}$

viii.60

ⓐ $a^{\frac{2}{5}}$ ⓑ ${\left(\mathrm{five}ab\right)}^{\frac{5}{\mathrm{iii}}}$
ⓒ ${\left(\frac{7xy}{z}\right)}^{\frac{3}{2}}$

8.61

ⓐ 9 ⓑ $\frac{1}{729}$ ⓒ $\frac{1}{8}$

8.62

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

viii.63

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

8.64

ⓐ $\mathrm{-729}$ ⓑ $-\frac{\mathrm{ane}}{729}$ ⓒ not a existent number

8.65

ⓐ $x^{\frac{3}{2}}$ ⓑ $x^{\mathrm{eight}}$ ⓒ $\frac{\mathrm{ane}}{\mathrm{10}}$

viii.66

ⓐ $y^{\frac{\mathrm{xi}}{\mathrm{eight}}}$ ⓑ ${\mathrm{thou}}^2$ ⓒ $\frac{1}{d}$

eight.67

ⓐ $8x^{\frac{\mathrm{one}}{5}}$ ⓑ ${\mathrm{10}}^{\frac{1}{2}}{y}^{\frac{1}{3}}$

viii.68

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

viii.70

ⓐ $u^{\mathrm{iii}}$ ⓑ $3{\mathrm{10}}^{\frac{\mathrm{one}}{5}}{y}^{\frac{\mathrm{one}}{3}}$

eight.71

ⓐ $\text{−}\sqrt{\mathrm{two}}$ ⓑ $11\sqrt[3]{\mathrm{ten}}$
ⓒ $3\sqrt[4]{x}-\mathrm{five}\sqrt[\mathrm{four}]{y}$

8.72

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

8.73

ⓐ $\mathrm{-2}\sqrt{7x}$ ⓑ $\text{−}\sqrt[4]{5xy}$

viii.74

ⓐ $\text{−}\sqrt{3y}$ ⓑ $3\sqrt[\mathrm{iii}]{7m\mathrm{north}}$

8.75

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

8.76

ⓐ $\mathrm{vii}\sqrt{3}$ ⓑ $\mathrm{-10}\sqrt[\mathrm{three}]{\mathrm{v}}$ ⓒ $\mathrm{-3}\sqrt[3]{2}$

eight.77

ⓐ $\text{−}{\mathrm{thousand}}^{\mathrm{three}}\sqrt{\mathrm{two}\mathrm{thousand}}$ ⓑ $x^{\mathrm{two}}\sqrt[3]{5x}$

8.78

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

8.79

ⓐ $12\sqrt{\mathrm{fifteen}}$ ⓑ $\mathrm{-18}\sqrt[3]{2}$

viii.80

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

viii.81

ⓐ $36{\mathrm{10}}^{\mathrm{iii}}\sqrt{5}$ ⓑ $\mathrm{viii}y\sqrt[4]{\mathrm{three}{y}^{\mathrm{ii}}}$

8.82

ⓐ $144y^2\sqrt{5y}$ ⓑ $\mathrm{-36}\sqrt[4]{\mathrm{iii}a}$

viii.83

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

8.84

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

8.85

ⓐ $\mathrm{-66}+\mathrm{fifteen}\sqrt{7}$
ⓑ $\sqrt[\mathrm{three}]{x^{\mathrm{two}}}-5\sqrt[\mathrm{three}]{\mathrm{10}}+\mathrm{six}$

8.86

ⓐ $41-14\sqrt{11}$
ⓑ $\sqrt[3]{{\mathrm{ten}}^{\mathrm{ii}}}+4\sqrt[3]{x}+\mathrm{iii}$

8.88

$\mathrm{-12}-\mathrm{twenty}\sqrt{3}$

8.89

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

viii.90

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

8.95

ⓐ $\frac{9x^{\mathrm{two}}}{y^{\mathrm{ii}}}$ ⓑ $\frac{\mathrm{-iv}\mathrm{ten}}{y}$

8.96

ⓐ $\frac{\mathrm{ten}{n}^{\mathrm{three}}}{m}$ ⓑ $\frac{\mathrm{-iii}p}{q^{\mathrm{two}}}$

8.99

ⓐ $\frac{5\sqrt{3}}{\mathrm{iii}}$ ⓑ $\frac{\sqrt{6}}{8}$ ⓒ $\frac{\sqrt{\mathrm{two}\mathrm{ten}}}{\mathrm{10}}$

8.100

ⓐ $\frac{6\sqrt{5}}{5}$ ⓑ $\frac{\sqrt{\mathrm{fourteen}}}{6}$ ⓒ $\frac{\sqrt{\mathrm{five}\mathrm{10}}}{x}$

8.101

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

8.102

ⓐ $\frac{\sqrt[\mathrm{three}]{4}}{2}$ ⓑ $\frac{\sqrt[\mathrm{iii}]{150}}{\mathrm{ten}}$ ⓒ $\frac{\mathrm{two}\sqrt[3]{5n^2}}{\mathrm{v}\mathrm{due\; north}}$

8.103

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

8.104

ⓐ $\frac{\sqrt[4]{125}}{\mathrm{v}}$ ⓑ $\frac{\sqrt[4]{224}}{\mathrm{eight}}$
ⓒ $\frac{\sqrt[4]{64x^{\mathrm{iii}}}}{x}$

8.105

$-\frac{\mathrm{iii}\left(\mathrm{ane}+\sqrt{\mathrm{v}}\right)}{4}$

viii.107

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

eight.108

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

viii.109

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

8.110

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

viii.113

$\text{no solution}$

8.114

$\text{no solution}$

eight.115

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

8.116

$y=5,y=6$

8.126

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

eight.130

$x=0x=4$

8.135

ⓐ $f\left(\mathrm{half\; dozen}\right)=4$ ⓑ no value at $\mathrm{10}=0$

8.136

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

8.137

ⓐ $\mathrm{yard}(4)=2$ ⓑ $\mathrm{grand}(\mathrm{i})=\mathrm{-1}$

8.138

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

8.139

ⓐ $f(\mathrm{four})=2$ ⓑ $f(\mathrm{-1})=1$

8.140

ⓐ $g(16)=3$ ⓑ $g(3)=2$

eight.141

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

viii.142

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

viii.143

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

8.144

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

8.145

$(\text{−}\infty ,\infty )$

eight.146

$(\text{−}\infty ,\infty )$

8.147

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

ⓒ range: $\left[0,\infty \right)$

8.148

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

ⓒ range: $\left[0,\infty \right)$

eight.149

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

ⓒ range: $\text{(}-\infty ,\infty )$

viii.150

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

ⓒ range: $\text{(}-\infty ,\infty )$

eight.151

ⓐ $9i$ ⓑ $\sqrt{\mathrm{v}}i$ ⓒ $\mathrm{three}\sqrt{2}i$

8.152

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

8.155

ⓐ $\mathrm{half-dozen}+5i$ ⓑ $6-3i$

8.156

ⓐ $\mathrm{-2}-6i$ ⓑ $2+9i$

8.157

$12+20i$

8.159

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

viii.160

$\mathrm{-v}-10i$

viii.161

$\mathrm{-21}-\mathrm{twenty}i$

eight.165

$\mathrm{-12}-22\sqrt{3}i$

8.166

$6+12\sqrt{\mathrm{two}}i$

eight.173

$\frac{\mathrm{four}}{17}+\frac{\mathrm{sixteen}}{17}i$

eight.174

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

viii.175

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

8.176

$\frac{\mathrm{four}}{5}-\frac{\mathrm{ii}}{5}i$

Section eight.1 Exercises

7.

ⓐ non real number ⓑ $\mathrm{-17}$

9.

ⓐ $\mathrm{-xv}$ ⓑ not real number

15.

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

17.

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

nineteen.

ⓐ $8<\sqrt{70}<9$
ⓑ $4<\sqrt[\mathrm{three}]{71}<\mathrm{five}$

21.

ⓐ $14<\sqrt{200}<15$
ⓑ $\mathrm{five}<\sqrt[\mathrm{three}]{137}<6$

23.

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

25.

ⓐ $7.28$ ⓑ $\approx \mathrm{v.28}$
ⓒ $\approx 4.61$

33.

ⓐ $x^{12}$ ⓑ $\left|y^{11}\right|$

39.

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

41.

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

47.

ⓐ $12\left|xy\right|$ ⓑ $13w^{\mathrm{four}}\left|y^{\mathrm{five}}\right|$
ⓒ $2a^{17}{b}^{\mathrm{two}}$

49.

ⓐ $11\left|ab\right|$ ⓑ $\mathrm{three}{c}^4{d}^{\mathrm{six}}$
ⓒ $4{\mathrm{10}}^5{y}^{22}$

Section eight.2 Exercises

67.

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

69.

ⓐ ${\mathrm{due\; north}}^{\mathrm{ten}}\sqrt{n}$ ⓑ $q^2\sqrt[3]{q^2}$
ⓒ $\left|\mathrm{due\; north}\right|\sqrt[\mathrm{viii}]{{\mathrm{northward}}^2}$

71.

ⓐ $\mathrm{five}{r}^{\mathrm{half\; dozen}}\sqrt[]{\mathrm{v}r}$ ⓑ $\mathrm{three}x\sqrt[3]{4x^2}$
ⓒ $2\left|y\right|\sqrt[\mathrm{four}]{\mathrm{iii}{y}^{\mathrm{ii}}}$

73.

ⓐ $11\left|m^{11}\right|\sqrt[]{\mathrm{two}\mathrm{one\; thousand}}$ ⓑ $3{\mathrm{1000}}^2\sqrt[\mathrm{four}]{5{\mathrm{grand}}^2}$ ⓒ $2\mathrm{northward}\sqrt[5]{5n^3}$

75.

ⓐ $7\left|{\mathrm{grand}}^{\mathrm{iii}}{\mathrm{northward}}^5\right|\sqrt[]{3\mathrm{yard}\mathrm{north}}$ ⓑ $\mathrm{ii}{x}^{\mathrm{ii}}{y}^2\sqrt[3]{\mathrm{half\; dozen}y}$ ⓒ $2\left|xy\right|\sqrt[4]{2x}$

77.

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

79.

ⓐ $\mathrm{-vi}\sqrt[\mathrm{iii}]{4}$ ⓑ not real

85.

ⓐ $\mathrm{one}+3\sqrt{5}$ ⓑ $1+\sqrt{10}$

91.

ⓐ $x^{\mathrm{ii}}$ ⓑ $p^3$ ⓒ $\left|q\right|$

93.

ⓐ $\frac{\mathrm{ane}}{y^2}$ ⓑ $u^{\mathrm{ii}}$ ⓒ $\left|5^3\right|$

95.

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

97.

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

99.

$\frac{\mathrm{seven}{r}^2\sqrt{2r}}{10}$

101.

$\frac{\mathrm{ii}\left|q^3\right|\sqrt{\mathrm{seven}}}{\mathrm{xv}}$

103.

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

105.

ⓐ $\frac{2\left|p^{\mathrm{three}}\right|\sqrt{7p}}{\left|q\right|}$ ⓑ $\frac{3s^2\sqrt[\mathrm{iii}]{\mathrm{three}{s}^{\mathrm{ii}}}}{t}$
ⓒ $\frac{2\left|p^{\mathrm{three}}\right|\sqrt[4]{\mathrm{iv}{p}^3}}{\left|q^3\right|}$

107.

ⓐ $\frac{\mathrm{four}\left|xy\right|}{3}$ ⓑ $\frac{y^2\sqrt[3]{x}}{2}$ ⓒ $\frac{\left|ab\right|\sqrt[4]{a}}{2}$

109.

ⓐ $\frac{\mathrm{one}}{\mathrm{two}\left|pq\right|}$ ⓑ $\frac{2cd\sqrt[3]{d^2}}{5}$
ⓒ $\frac{\left|\mathrm{grand}n\right|}{2}$

111.

ⓐ $\frac{\mathrm{iii}{p}^{\mathrm{four}}\sqrt{p}}{\left|q\right|}$ ⓑ $2\sqrt[\mathrm{iv}]{2}$
ⓒ $2\mathrm{ten}\sqrt[\mathrm{v}]{\mathrm{two}\mathrm{ten}}$

113.

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

Section viii.3 Exercises

121.

ⓐ $\sqrt[\mathrm{v}]{u}$ ⓑ $\sqrt[9]{v}$ ⓒ $\sqrt[\mathrm{twenty}]{\mathrm{due\; west}}$

123.

ⓐ $\frac{\mathrm{ane}}{x^7}$ ⓑ $\frac{1}{y^9}$ ⓒ $f^{\frac{\mathrm{i}}{\mathrm{five}}}$

125.

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

127.

ⓐ ${\left(21p\right)}^{\frac{\mathrm{ane}}{\mathrm{ii}}}$ ⓑ ${\left(8q\right)}^{\frac{1}{4}}$
ⓒ $4{\left(36r\right)}^{\frac{\mathrm{one}}{6}}$

133.

ⓐ $\mathrm{-six}$ ⓑ $\mathrm{-6}$ ⓒ $\frac{\mathrm{i}}{6}$

135.

ⓐ not real ⓑ $\mathrm{-3}$ ⓒ $\frac{\mathrm{one}}{\mathrm{three}}$

137.

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

139.

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

141.

ⓐ $m^{\frac{\mathrm{five}}{\mathrm{ii}}}$ ⓑ ${\left(3y\right)}^{\frac{\mathrm{vii}}{\mathrm{three}}}$ ⓒ ${\left(\frac{\mathrm{iv}x}{5y}\right)}^{\frac{\mathrm{three}}{\mathrm{five}}}$

143.

ⓐ $u^{\frac{2}{5}}$ ⓑ ${\left(\mathrm{half-dozen}x\right)}^{\frac{\mathrm{v}}{\mathrm{iii}}}$ ⓒ ${\left(\frac{18a}{5b}\right)}^{\frac{\mathrm{vii}}{4}}$

145.

ⓐ 32,768 ⓑ $\frac{1}{729}$ ⓒ ix

147.

ⓐ 4 ⓑ $\frac{1}{9}$ ⓒ non real

149.

ⓐ $\mathrm{-27}$ ⓑ $-\frac{1}{27}$ ⓒ not existent

151.

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

153.

ⓐ $y^{\frac{5}{\mathrm{iv}}}$ ⓑ ${\mathrm{ten}}^8$ ⓒ $\frac{\mathrm{i}}{m}$

155.

ⓐ $81q^{\mathrm{two}}$ ⓑ $a^{\frac{1}{2}}b$

157.

ⓐ $8u^{\frac{1}{\mathrm{four}}}$ ⓑ $\mathrm{viii}{p}^{\frac{1}{2}}{q}^{\frac{\mathrm{three}}{4}}$

Section 8.four Exercises

165.

ⓐ $3\sqrt{2}$ ⓑ $7\sqrt[3]{k}$ ⓒ $\mathrm{vi}\sqrt[\mathrm{iv}]{\mathrm{thou}}$

167.

ⓐ $9\sqrt{5}$ ⓑ $12\sqrt[\mathrm{three}]{a}$ ⓒ $\mathrm{six}\sqrt[4]{2z}$

173.

ⓐ $-2\sqrt{3}$ ⓑ $\mathrm{-2}\sqrt[3]{5}$ ⓒ $3\sqrt[\mathrm{iv}]{2}$

175.

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

179.

ⓐ $2c^{\mathrm{iii}}\sqrt{5c}$ ⓑ $\mathrm{fourteen}{r}^2\sqrt[\mathrm{iv}]{\mathrm{ii}{r}^{\mathrm{two}}}$

183.

ⓐ $\mathrm{-18}\sqrt{6}$ ⓑ $\mathrm{-64}\sqrt[\mathrm{iii}]{\mathrm{ix}}$

185.

ⓐ $\mathrm{-30}\sqrt{2}$ ) ⓑ $\mathrm{half-dozen}\sqrt[4]{\mathrm{two}}$

187.

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

189.

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

191.

ⓐ $14+5\sqrt{\mathrm{vii}}$ ⓑ $4\sqrt[3]{6}+\mathrm{three}\sqrt[3]{4}$

193.

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

197.

ⓐ $30+\mathrm{eighteen}\sqrt{2}$ ⓑ $\sqrt[3]{{\mathrm{ten}}^2}-\mathrm{two}\sqrt[3]{x}-\mathrm{iii}$

199.

ⓐ $\mathrm{-55}+\mathrm{thirteen}\sqrt{10}$
ⓑ $2\sqrt[3]{x^2}+\mathrm{viii}\sqrt[3]{x}+\mathrm{half\; dozen}$

203.

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

205.

ⓐ $14+6\sqrt{5}$ ⓑ $79-20\sqrt{3}$

207.

ⓐ $87-18\sqrt{6}$
ⓑ $163+60\sqrt{7}$

215.

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

223.

$10c^2\sqrt{\mathrm{iii}}-9c^{\mathrm{three}}\sqrt{\mathrm{iii}}$

Section eight.v Exercises

251.

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

253.

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

257.

$2ab\sqrt[\mathrm{iii}]{2a}$

259.

ⓐ $\frac{5\sqrt{\mathrm{half-dozen}}}{3}$ ⓑ $\frac{2\sqrt{\mathrm{iii}}}{9}$ ⓒ $\frac{2\sqrt{5x}}{x}$

261.

ⓐ $\frac{\mathrm{half\; dozen}\sqrt{\mathrm{vii}}}{7}$ ⓑ $\frac{\mathrm{ii}\sqrt{\mathrm{x}}}{\mathrm{fifteen}}$ ⓒ $\frac{4\sqrt{3p}}{p}$

263.

ⓐ $\frac{\sqrt[3]{25}}{5}$ ⓑ $\frac{\sqrt[\mathrm{iii}]{45}}{\mathrm{half\; dozen}}$ ⓒ $\frac{2\sqrt[3]{6a^{\mathrm{two}}}}{\mathrm{iii}a}$

265.

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

267.

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

269.

ⓐ $\frac{\sqrt[\mathrm{four}]{\mathrm{nine}}}{3}$ ⓑ $\frac{\sqrt[4]{\mathrm{fifty}}}{4}$ ⓒ $\frac{\mathrm{ii}\sqrt[4]{\mathrm{three}{a}^2}}{a}$

271.

$\mathrm{-2}\left(1+\sqrt{5}\right)$

273.

$\mathrm{iii}\left(3+\sqrt{7}\right)$

275.

$\frac{\sqrt{\mathrm{iii}}\left(\sqrt{\mathrm{1000}}+\sqrt{5}\right)}{m-5}$

277.

$\frac{\sqrt{2}\left(\sqrt{x}+\sqrt{\mathrm{vi}}\right)}{x-6}$

279.

${\frac{\left(\sqrt{r}+\sqrt{\mathrm{five}}\right)}{r-5}}^{\mathrm{ii}}$

281.

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

Section 8.6 Exercises

301.

$u=3,u=4$

303.

$r=1,r=2$

329.

$\mathrm{ten}=\mathrm{-8},x=2$

337.

$\mathrm{ten}=0x=4$

339.

$x=1x=\mathrm{five}$

Department 8.7 Exercises

351.

ⓐ $f(\mathrm{five})=4$ ⓑ no value at $\mathrm{10}=0$

353.

ⓐ $g(4)=\mathrm{five}$ ⓑ $\mathrm{yard}(8)=7$

355.

ⓐ $F(1)=\mathrm{ane}$ ⓑ $F(\mathrm{-11})=5$

357.

ⓐ $G(5)=2\sqrt{6}$ ⓑ $\mathrm{Thousand}(2)=\mathrm{three}$

359.

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

361.

ⓐ $h(\mathrm{-ii})=0$ ⓑ $h(6)=2\sqrt[\mathrm{iii}]{\mathrm{four}}$

363.

ⓐ $f(0)=0$ ⓑ $f(2)=\mathrm{two}$

365.

ⓐ $g(1)=0$ ⓑ $\mathrm{one\; thousand}(\mathrm{-3})=2$

367.

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

369.

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

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: $\left[\mathrm{-4},\infty \right)$
ⓑ

ⓒ $\left[0,\infty \right)$

387.

ⓐ domain: $\left[0,\infty \right)$
ⓑ

ⓒ $\left[2,\infty \right)$

389.

ⓐ domain: $\left[0,\infty \right)$
ⓑ

ⓒ $\left[0,\infty \right)$

391.

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

ⓒ $\left[0,\infty \right)$

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

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

Section 8.8 Exercises

409.

ⓐ $\mathrm{four}i$ ⓑ $\sqrt{11}i$ ⓒ $2\sqrt{\mathrm{two}}i$

411.

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

427.

$25-2\sqrt{2}i$

431.

$\mathrm{-12}+18i$

433.

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

445.

$\mathrm{-44}+4\sqrt{\mathrm{three}}i$

447.

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

459.

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

461.

$\frac{6}{13}+\frac{\mathrm{nine}}{13}i$

463.

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

465.

$\frac{4}{3}-\frac{\mathrm{ane}}{3}i$

467.

$-\frac{\mathrm{three}}{4}+\frac{1}{\mathrm{two}}i$

Review Exercises

485.

ⓐ $8<\sqrt{68}<9$
ⓑ $\mathrm{four}<\sqrt[3]{84}<\mathrm{five}$

497.

ⓐ $4\left|s^7\right|\sqrt[]{\mathrm{five}s}$ ⓑ $2a\sqrt[\mathrm{five}]{3a^2}$
ⓒ $\mathrm{two}\left|b\right|\sqrt[6]{2b}$

501.

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

503.

$\frac{\mathrm{ten}{m}^2\sqrt{3m}}{\mathrm{viii}}$

505.

ⓐ $\frac{\mathrm{ane}}{\mathrm{two}\left|pq\right|}$ ⓑ $\frac{2cd\sqrt[\mathrm{v}]{2d^2}}{\mathrm{five}}$
ⓒ $\frac{\left|mn\right|\sqrt[\mathrm{vi}]{2}}{2}$

511.

ⓐ $\mathrm{-2}$ ⓑ $\frac{1}{\mathrm{iii}}$ ⓒ $\mathrm{-five}$

515.

ⓐ ${\mathrm{half-dozen}}^3$ ⓑ $b^{\mathrm{ix}}$ ⓒ $\frac{\mathrm{ane}}{w}$

517.

ⓐ $4\sqrt{2}$ ⓑ $9\sqrt[\mathrm{three}]{p}$ ⓒ $\mathrm{ii}\sqrt[\mathrm{three}]{\mathrm{ten}}$

519.

ⓐ $7\sqrt{3}$ ⓑ $7\sqrt[\mathrm{iii}]{2}$ ⓒ $3\sqrt[\mathrm{four}]{5}$

523.

ⓐ $126{\mathrm{ten}}^2\sqrt{2}$ ⓑ $48a\sqrt[3]{a^2}$

525.

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

527.

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

529.

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

531.

ⓐ $\frac{\mathrm{eight}{\mathrm{one\; thousand}}^4}{3n^{\mathrm{iv}}}$ ⓑ $-\frac{x^2}{\mathrm{two}{y}^{\mathrm{two}}}$

533.

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

535.

$-\frac{\mathrm{vii}\left(2+\sqrt{6}\right)}{2}$

537.

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

541.

$u=\mathrm{three},u=\mathrm{four}$

547.

$\mathrm{10}=\mathrm{-8},x=2$

553.

ⓐ $\mathrm{Thousand}(5)=2\sqrt{\mathrm{half\; dozen}}$ ⓑ $G(2)=\mathrm{three}$

555.

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

559.

$\left[\frac{7}{\mathrm{x}},\infty \right)$

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 Examination

581.

$2x^2{y}^{}\sqrt[\mathrm{three}]{\mathrm{nine}{x}^{\mathrm{ii}}y}$

593.

$\frac{7{\mathrm{10}}^5}{3y^{\mathrm{vii}}}$

595.

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

603.

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

ⓒ range: $\left[0,\infty \right)$

Chapter 8 Test Algebra 1,

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

Posted by: arringtonungazintonat.blogspot.com

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