Chapter 9

ⓐ $\mathrm{-7}$ ⓑ $15$

ⓐ $8$ ⓑ $\mathrm{-11}$

ⓐ not a real number ⓑ $\mathrm{-9}$

ⓐ $\mathrm{-7}$ ⓑ not a real number

ⓐ 7 ⓑ 5

ⓐ 17 ⓑ $23$

$6<\sqrt{38}<7$

$9<\sqrt{84}<10$

$\approx 3.32$

$\approx 3.61$

ⓐ $y^4$ ⓑ $z^6$

ⓐ $m^2$ ⓑ $b^5$

$8x$

$13y$

$\mathrm{-11}y$

$\mathrm{-10}p$

$10ab$

$15mn$

$7x^{15}$

$9w^{18}$

$13x^5{y}^7$

$12p^6{q}^{10}$

$4\sqrt{3}$

$3\sqrt{5}$

$12\sqrt{2}$

$12\sqrt{3}$

$b^2\sqrt{b}$

$p^4\sqrt{p}$

$4x^3\sqrt{x}$

$7v^4\sqrt{v}$

$4y^2\sqrt{2y}$

$5a^4\sqrt{3a}$

$7a^3{b}^2{\sqrt{2ab}}^{}$

$6m^4{n}^5\sqrt{5mn}$

$5+5\sqrt{3}$

$2+7\sqrt{2}$

$2-\sqrt{3}$

$2-\sqrt{5}$

$\frac{5}{4}$

$\frac{7}{9}$

$\frac{5}{4}$

$\frac{7}{9}$

$a$

$x^2$

$5x^2$

$6z$

$\frac{\sqrt{19}}{7}$

$\frac{2\sqrt{7}}{9}$

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

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

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

$\frac{3u^3\sqrt{6u}}{v^4}$

$\frac{8x^2}{3}$

$\frac{2a^2}{5}$

$\frac{5y\sqrt{x}}{6}$

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

$\text{−}\sqrt{2}$

$\mathrm{-4}\sqrt{3}$

$9\sqrt{x}$

$8\sqrt{u}$

$7\sqrt{p}-6\sqrt{q}$

$6\sqrt{a}-3\sqrt{b}$

$9\sqrt{11}$

$11\sqrt{10}$

$\sqrt{5}+2\sqrt{6}$

$\mathrm{-5}\sqrt{7}+2\sqrt{5}$

$\mathrm{-2}\sqrt{7x}$

$\text{−}\sqrt{3y}$

$\mathrm{-2}\sqrt{5xy}$

$0$

$9\sqrt{2}$

$7\sqrt{3}$

$\sqrt{2}$

$\text{−}\sqrt{5}$

$6\sqrt{3}$

$\mathrm{-15}\sqrt{5}$

$\text{−}\sqrt{3}$

$0$

$\frac{14}{15}\sqrt{2}$

$\frac{1}{12}\sqrt{5}$

$\text{−}{m}^3\sqrt{2m}$

$\text{−}p\sqrt{3p}$

$20x\sqrt{2}-12x\sqrt{3}$

$28y\sqrt{3}-24y\sqrt{2}$

$10x\sqrt{3}$

$\mathrm{-5}x\sqrt{2}$

ⓐ $3\sqrt{2}$ ⓑ $36\sqrt{2}$

ⓐ $5\sqrt{2}$ ⓑ $90\sqrt{2}$

$12\sqrt{15}$

$27\sqrt{2}$

ⓐ $3x^2\sqrt{2}$ ⓑ $10y^2\sqrt{y}$

ⓐ $2x^3\sqrt{3}$ ⓑ $6y^2\sqrt{y}$

$144x^3\sqrt{10}$

$144y^2\sqrt{5y}$

ⓐ 12 ⓑ $15$

ⓐ 16 ⓑ 20

ⓐ 330 ⓑ 200

ⓐ 210 ⓑ 96

ⓐ $6-2\sqrt{5}$ ⓑ $2\sqrt{3}-3\sqrt{6}$

ⓐ $12+6\sqrt{6}$ ⓑ $\sqrt{7}+7\sqrt{2}$

ⓐ $18+\sqrt{6}$ ⓑ $6+12\sqrt{2}$

ⓐ $\mathrm{-40}+4\sqrt{2}$ ⓑ $2\sqrt{7}+14\sqrt{3}$

$\mathrm{-3}+2\sqrt{6}$

$\mathrm{-2}+2\sqrt{10}$

$\mathrm{-66}+15\sqrt{7}$

$41+14\sqrt{11}$

$1+9\sqrt{21}$

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

$12-8\sqrt{m}-15m$

$10-47\sqrt{n}-15n$

ⓐ $102+20\sqrt{2}$ ⓑ $55+6\sqrt{6}$

ⓐ $31-12\sqrt{5}$ ⓑ $121-36\sqrt{10}$

$4+20\sqrt{m}+25m$

$9-24\sqrt{n}+16n$

$1$

$\mathrm{-4}$

$\mathrm{-11}$

$\mathrm{-159}$

$\frac{\sqrt{2}}{2}$

$\frac{\sqrt{3}}{3}$

$\frac{4-\sqrt{10}}{5}$

$\frac{5-\sqrt{3}}{4}$

$\frac{2}{3}$

$\frac{4}{3}$

$n\sqrt{2}$

$p^2\sqrt{7}$

$\frac{5s}{8}$

$\frac{5q^2}{6}$

$\frac{9x^2}{y^2}$

$\frac{10n^3}{m}$

$\frac{5\sqrt{3}}{3}$

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

$\frac{\sqrt{5}}{2}$

$-\frac{3\sqrt{3}}{4}$

$\frac{\sqrt{14}}{6}$

$\frac{\sqrt{6}}{8}$

$\frac{1}{3}$

$\frac{\sqrt{5}}{5}$

$\frac{2\left(2-\sqrt{3}\right)}{1}$

$\frac{5\left(5-\sqrt{3}\right)}{22}$

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

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

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

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

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

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

ⓐ no ⓑ $\text{yes}$

ⓐ no ⓑ $\text{yes}$

$10$

$7$

$\frac{23}{3}$

$\frac{3}{10}$

$\frac{1}{2}$

$\frac{3}{5}$

$\text{no solution}$

$\text{no solution}$

$2,3$

$5,6$

$7$

$3$

$\frac{127}{2}$

$\frac{311}{3}$

no solution

no solution

$\text{no solution}$

$\text{no solution}$

$\text{no solution}$

$\text{no solution}$

$19.2\text{yards}$

$52.0\text{cm}$

$9\text{seconds}$

$3.5\text{seconds}$

$42.7\text{feet}$

$54.1\text{feet}$

ⓐ 3 ⓑ 4 ⓒ 3

ⓐ 10 ⓑ 2 ⓒ 2

ⓐ $\mathrm{-5}$ ⓑ not real ⓒ $\mathrm{-2}$

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

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

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

ⓐ $u^3$ ⓑ $v^5$

ⓐ $c^4$ ⓑ $d^4$

ⓐ $3x^9$ ⓑ $3\left|q^7\right|$

ⓐ $5p^3$ ⓑ $3q^5$

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

ⓐ $p\sqrt[5]{p^3}$ ⓑ $q^2\sqrt[6]{q}$

ⓐ $3\sqrt[3]{4}$ ⓑ $2\sqrt[4]{4}$

ⓐ $5\sqrt[3]{5}$ ⓑ $3\sqrt[4]{9}$

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

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

ⓐ $\mathrm{-3}\sqrt[3]{4}$ ⓑ $\text{not real}$

ⓐ $\mathrm{-5}\sqrt[3]{5}$ ⓑ $\text{not real}$

ⓐ $\left|x\right|$ ⓑ $y^3$

ⓐ $m^2$ ⓑ $n^2$

ⓐ $\text{not real}$ ⓑ $3\left|m\right|\sqrt[4]{2m^2}$

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

ⓐ $\frac{3c^3\sqrt[3]{4c}}{d^2}$ ⓑ $\frac{x^2}{\left|y\right|}\sqrt[4]{\frac{80x^2}{y}}$

ⓐ $r\sqrt[3]{\frac{40}{s}}$ ⓑ $\frac{3m^3\sqrt[4]{2m^2}}{\left|n^3\right|}$

ⓐ $2\sqrt[5]{3x}$ ⓑ $2\sqrt[3]{9}$

ⓐ $2\sqrt[4]{10y}$ ⓑ $2\sqrt[6]{32}$

ⓐ $\sqrt[3]{3}$ ⓑ $6\sqrt[4]{2}$

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

ⓐ $2y\sqrt[3]{4y^2}+3y^2\sqrt[3]{4y^2}$ ⓑ $3r^2\sqrt[4]{3r^3}+4r^2\sqrt[4]{3r^2}$

ⓐ $2z^2\sqrt[3]{5z}+3z\sqrt[3]{5z}$ ⓑ $2\left|s^3\right|\sqrt[4]{5s}+4\left|s\right|\sqrt[4]{5s}$

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

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

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

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

ⓐ ${(10m)}^{\frac{1}{2}}$ ⓑ ${(3n)}^{\frac{1}{5}}$ ⓒ ${(486y)}^{\frac{1}{4}}$

ⓐ ${(3k)}^{\frac{1}{7}}$ ⓑ ${(5j)}^{\frac{1}{4}}$ ⓒ ${(1024a)}^{\frac{1}{3}}$

ⓐ 6 ⓑ 2 ⓒ 2

ⓐ 10 ⓑ 3 ⓒ 3

ⓐ $\mathrm{-5}$ ⓑ $\mathrm{-5}$ ⓒ $\frac{1}{5}$

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

ⓐ $\mathrm{-8}$ ⓑ $\mathrm{-8}$ ⓒ $\frac{1}{8}$

ⓐ $\mathrm{-4}$ ⓑ $\mathrm{-4}$ ⓒ $\frac{1}{4}$

ⓐ $x^{\frac{5}{2}}$ ⓑ $z^{\frac{3}{4}}$ ⓒ $y^{\frac{2}{5}}$

ⓐ $a^{\frac{2}{5}}$ ⓑ $b^{\frac{7}{3}}$ ⓒ $m^{\frac{5}{4}}$

ⓐ 8 ⓑ 9 ⓒ 125

ⓐ 32 ⓑ 729 ⓒ 8

ⓐ $\frac{1}{32}$ ⓑ $\frac{1}{729}$ ⓒ $\frac{1}{8}$

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

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

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

ⓐ 9 ⓑ $y^3$ ⓒ m

ⓐ 25 ⓑ z ⓒ n

ⓐ $p^2$ ⓑ $q^6$ ⓒ $x^8$

ⓐ $r^{10}$ ⓑ $s^9$ ⓒ $m^2$

ⓐ u ⓑ $v^{\frac{1}{5}}$ ⓒ $\frac{1}{x}$

ⓐ $c^6$ ⓑ $\frac{1}{m}$ ⓒ $\frac{1}{d}$

ⓐ $8x^{\frac{1}{5}}$ ⓑ $4y^{\frac{2}{9}}$

ⓐ $64m^{\frac{1}{2}}$ ⓑ $729n^{\frac{3}{5}}$

ⓐ $m^2$ ⓑ $n^3$

ⓐ $u^3$ ⓑ $v^5$

6

8

3

10

$\mathrm{-2}$

$\mathrm{-1}$

not a real number

not a real number

5

7

$8<\sqrt{70}<9$

$14<\sqrt{200}<15$

4.36

7.28

$y$

$a^7$

$7x$

$11m^{10}$

$9x^{18}$

$\mathrm{-9}{x}^9$

$\mathrm{-8}a$

$12xy$

$13w^4{y}^5$

$3c^4{d}^6$

25 centimeters

Answers will vary.

$3\sqrt{3}$

$5\sqrt{5}$

$10\sqrt{2}$

$15\sqrt{2}$

$20\sqrt{2}$

$15\sqrt{3}$

$x^3\sqrt{x}$

$p\sqrt{p}$

$m^6\sqrt{m}$

$r^{12}\sqrt{r}$

$7n^8\sqrt{n}$

$9r^7\sqrt{r}$

$7m^2\sqrt{2m}$

$5r^6\sqrt{5r}$

$10p^6\sqrt{2p}$

$11m^{11}\sqrt{2m}$

$7m^3{n}^5\sqrt{3mn}$

$5r^6{s}^4\sqrt{3rs}$ 70)

$10p^4{q}^5\sqrt{3pq}$

$11m^6{n}^{10}\sqrt{2mn}$

$5+2\sqrt{3}$

$1+3\sqrt{5}$

$5-2\sqrt{6}$

$1+\sqrt{10}$

$\frac{7}{8}$

$\frac{11}{4}$

$\frac{6}{7}$

$\frac{3}{5}$

$x^2$

$\frac{1}{y^2}$

$10x^2$

$4p^4$

$\frac{6}{\sqrt{35}}$

$\frac{2\sqrt{5}}{9}$

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

$\frac{10m^2\sqrt{3m}}{8}$

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

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

$\frac{5r^4\sqrt{3r}}{s^4}$

$\frac{4p^3\sqrt{7p}}{q}$

$\frac{5x}{3}$