Chapter 8

ⓐ $\mathrm{-8}$ ⓑ 15

ⓐ 10 ⓑ $\mathrm{-11}$

ⓐ not a real number ⓑ $\mathrm{-9}$

ⓐ $\mathrm{-7}$ ⓑ not a real number

ⓐ 3 ⓑ 4 ⓒ 3

ⓐ 10 ⓑ 2 ⓒ 3

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

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

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

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

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

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

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

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

ⓐ $\left|y^9\right|$ ⓑ $z^6$

ⓐ $m^2$ ⓑ $\left|b^5\right|$

ⓐ $\left|u^3\right|$ ⓑ $v^5$

ⓐ $c^4$ ⓑ $d^4$

ⓐ $8\left|x\right|$ ⓑ $\mathrm{-10}\left|p\right|$

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

ⓐ $3x^9$ ⓑ $3\left|q^7\right|$

ⓐ $5p^3$ ⓑ $3q^5$

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

ⓐ $15\left|mn\right|$ ⓑ $13\left|x^5{y}^7\right|$
ⓒ $3w^{12}{z}^5$

$4\sqrt{3}$

$3\sqrt{5}$

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

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

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

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

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

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

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

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

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

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

ⓐ $5+5\sqrt{3}$ ⓑ $2-\sqrt{3}$

ⓐ $2+7\sqrt{2}$ ⓑ $2-\sqrt{5}$

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

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

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

ⓐ $x^2$ ⓑ $m^2$ ⓒ $n^2$

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

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

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

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

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

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

ⓐ $7z^2$ ⓑ $\mathrm{-5}\sqrt[3]{2}$
ⓒ $3\left|m\right|\sqrt[4]{2m^2}$

ⓐ $8m^4$ ⓑ $\mathrm{-4}$ ⓒ $3\left|n\right|\sqrt[4]{2}$

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

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

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

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

ⓐ 6 ⓑ 2 ⓒ 2

ⓐ 10 ⓑ 3 ⓒ 3

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

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

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

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

ⓐ 9 ⓑ $\frac{1}{729}$ ⓒ $\frac{1}{8}$

ⓐ 8 ⓑ $\frac{1}{9}$ ⓒ $\frac{1}{125}$

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

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

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

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

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

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

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

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

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

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

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

ⓐ $\text{−}\sqrt{3y}$ ⓑ $3\sqrt[3]{7mn}$

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

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

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

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

ⓐ $12\sqrt{15}$ ⓑ $\mathrm{-18}\sqrt[3]{2}$

ⓐ $27\sqrt{2}$ ⓑ $\mathrm{-36}\sqrt[3]{2}$

ⓐ $36x^3\sqrt{5}$ ⓑ $8y\sqrt[4]{3y^2}$

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

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

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

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

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

$1+9\sqrt{21}$

$\mathrm{-12}-20\sqrt{3}$

ⓐ $102+20\sqrt{2}$ ⓑ $55+6\sqrt{6}$

ⓐ $41-12\sqrt{5}$
ⓑ $121-36\sqrt{10}$

$\mathrm{-11}$

$\mathrm{-159}$

ⓐ $\frac{5s}{8}$ ⓑ $\frac{2}{a}$

ⓐ $\frac{5q^2}{6}$ ⓑ $\frac{2}{b}$

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

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

$4xy\sqrt{2x}$

$4ab\sqrt{3b}$

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

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

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

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

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

ⓐ $\frac{\sqrt[4]{125}}{5}$ ⓑ $\frac{\sqrt[4]{224}}{8}$
ⓒ $\frac{\sqrt[4]{64x^3}}{x}$

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

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

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

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

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

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

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

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

$\text{no solution}$

$\text{no solution}$

$x=2,x=3$

$y=5,y=6$

$x=\mathrm{-6}$

$x=\mathrm{-9}$

$x=8$

$x=6$

$m=7$

$n=3$

$a=63$

$b=311$

$x=3$

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

$x=4$

$x=9$

$x=5$

$x=0x=4$

9 seconds

$3.5$ seconds

$42.7$ feet

$54.1$ feet

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

ⓐ $g\left(4\right)=5$ ⓑ no value at $f(\mathrm{-3})$

ⓐ $g(4)=2$ ⓑ $g(1)=\mathrm{-1}$

ⓐ $h(2)=2$
ⓑ $h(\mathrm{-5})=\mathrm{-3}$

ⓐ $f(4)=2$ ⓑ $f(\mathrm{-1})=1$

ⓐ $g(16)=3$ ⓑ $g(3)=2$

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

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

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

$\left(5,\infty \right)$

$(\text{−}\infty ,\infty )$

$(\text{−}\infty ,\infty )$

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

ⓒ range: $\left[0,\infty \right)$

ⓐ domain: $\left[2,\infty \right)$
ⓑ

ⓒ range: $\left[0,\infty \right)$

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

ⓒ range: $\text{(}-\infty ,\infty )$

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

ⓒ range: $\text{(}-\infty ,\infty )$

ⓐ $9i$ ⓑ $\sqrt{5}i$ ⓒ $3\sqrt{2}i$

ⓐ $6i$ ⓑ $\sqrt{3}i$ ⓒ $3\sqrt{3}i$

$6\sqrt{2}i$

$7\sqrt{3}i$

ⓐ $6+5i$ ⓑ $6-3i$

ⓐ $\mathrm{-2}-6i$ ⓑ $2+9i$

$12+20i$

$12+6i$

$\mathrm{-11}-7i$

$\mathrm{-5}-10i$

$\mathrm{-21}-20i$

$9-40i$

$\mathrm{-14}$

$\mathrm{-54}$

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

$6+12\sqrt{2}i$

25

29

109

41

i

i

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

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

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

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

$\text{−}i$

$1$

ⓐ 8 ⓑ $\mathrm{-9}$

ⓐ 14 ⓑ $\mathrm{-1}$

ⓐ $\frac{2}{3}$ ⓑ $\mathrm{-0.1}$

ⓐ not real number ⓑ $\mathrm{-17}$

ⓐ $\mathrm{-15}$ ⓑ not real number

ⓐ 6 ⓑ 4

ⓐ 8 ⓑ 3 ⓒ 1

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

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

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

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

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

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

ⓐ u ⓑ $\left|v\right|$

ⓐ $\left|y\right|$ ⓑ $m$

ⓐ $\left|x^3\right|$ ⓑ $y^8$

ⓐ $x^{12}$ ⓑ $\left|y^{11}\right|$

ⓐ $x^3$ ⓑ $\left|y^3\right|$

ⓐ $m^2$ ⓑ $n^4$

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

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

ⓐ $2x^2$ ⓑ $2y^2$

ⓐ $6a^2$ ⓑ $2b^4$

ⓐ $12\left|xy\right|$ ⓑ $13w^4\left|y^5\right|$
ⓒ $2a^{17}{b}^2$