9.8 Exercise supplement

$\sqrt{10}\sqrt{2}$

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

$\sqrt{18}\sqrt{40}$

$\sqrt{11}\sqrt{11}$

$\sqrt{y}\sqrt{y}$

$\sqrt{r^3}\sqrt{r^3}$

$\sqrt{m+3}\sqrt{m+3}$

$\sqrt{a-7}\sqrt{a-7}$

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

$\sqrt{y^2-12y+36}$

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

$\frac{\sqrt{n-3}}{\sqrt{n-1}}$

$\frac{\sqrt{50}}{\sqrt{2}}$

$\frac{\sqrt{75}}{5\sqrt{3}}$

$\frac{\sqrt{a^2+6a+9}}{\sqrt{a+3}}$

$\frac{\sqrt{4x^2+4x+1}}{\sqrt{2x+1}}$

$\frac{\sqrt{x^2-11x+24}}{\sqrt{x-8}}$

$\frac{\sqrt{y^2+11y+28}}{\sqrt{y+4}}$

$\sqrt{3}\left(\sqrt{5}+\sqrt{3}\right)$

$\sqrt{5}\left(\sqrt{6}-\sqrt{10}\right)$

$\sqrt{a}\left(\sqrt{a}-\sqrt{bc}\right)$

$\sqrt{x}\left(\sqrt{x^5}-\sqrt{3x}\right)$

$\sqrt{7a^3}\left(\sqrt{2a}-\sqrt{4a^3}\right)$

$\frac{3}{\sqrt{7}}$

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

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

$\frac{8y}{\sqrt{y}}$

$\frac{16a^2}{\sqrt{5a}}$

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

$\left(x+\sqrt{8}\right)\left(3x+\sqrt{8}\right)$

$\left(4y-\sqrt{3x}\right)\left(4y+\sqrt{3x}\right)$

$\left(6r+\sqrt{2s}\right)\left(4r+\sqrt{2s}\right)$

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

$\frac{4}{1-\sqrt{6}}$

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

$\frac{10}{a-\sqrt{2b}}$

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

$\frac{\sqrt{2}}{1+\sqrt{10}}$

$\frac{8+\sqrt{3}}{2+\sqrt{6}}$

$\frac{4+\sqrt{11}}{4-\sqrt{11}}$

$\sqrt{\frac{36a^4{b}^5{c}^{11}}{x^2{y}^5}}$

$\sqrt{x^{12}{y}^{10}{z}^8{w}^7}$

$\sqrt{32x^{5}y{\left(x-2\right)}^3}$

$-2\sqrt{60r^4{s}^3}$

$\sqrt{\frac{3}{16}}$

$\sqrt{\frac{4}{25}}$

$\sqrt{\frac{9}{16}}$

$\sqrt{\frac{5}{36}}$

$\sqrt{\frac{1}{6}}$

$\sqrt{\frac{3}{10}}$

$\sqrt{{\left(x+4\right)}^4{\left(x-1\right)}^5}$

$\sqrt{{\left(3x+5\right)}^3{\left(2x-7\right)}^3}$

$\sqrt{{\left(y-3z\right)}^{12}{\left(y+3z\right)}^{10}{\left(y-5z\right)}^3}$

$\sqrt{{\left(8a-5b\right)}^{26}{\left(2a-9b\right)}^{40}{\left(a-b\right)}^{15}}$

$4\sqrt{11}+8\sqrt{11}$

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

$5\sqrt{60}-7\sqrt{15}$

$4a{x}^2\sqrt{75x^4}+6a\sqrt{3x^8}$

$-3\sqrt{54}-16\sqrt{96}$

$\sqrt{18x^{2}y}\sqrt{2x^{2}y}$

$\sqrt{4x^2+32x+64}+\sqrt{10x^2+80x+160}$

$-2\sqrt{9x^2-42x+49}+5\sqrt{18x^2-84x+98}$

$-10\sqrt{56a^3{b}^7}+2a^{2}b\sqrt{126a{b}^5}$

$\frac{\sqrt{3x}-\sqrt{5x}}{\sqrt{7x}+\sqrt{2x}}$

$\frac{\sqrt{6a}+\sqrt{2a}}{\sqrt{3a}-\sqrt{5a}}$

$\sqrt{3x}=9$

$\sqrt{4a}=16$

$\sqrt{x}+7=4$

$\sqrt{a+6}=-5$

$\sqrt{4a+5}=21$

$\sqrt{3m+7}=10$

$\sqrt{y+10}=5$

$\sqrt{a-7}=6$

$\sqrt{4x-8}=x-2$

$\sqrt{2x+3}+8=11$

$\sqrt{a^2+5}+5=a$

$\sqrt{5b+4}-5=-2$

$\sqrt{2a+1}-10=-3$

$\sqrt{2x+5}=\sqrt{x+3}$

$\sqrt{5a-11}$

At a small business, the monthly number of sales $S$ is approximately related to the number of employees $E$ by $S=140+8\sqrt{E-2}.$

(a) Determine the approximate number of sales if the number of employees is 27.

(b) Determine the approximate number of employees if the monthly sales are 268.

The resonance frequency $f$ in an electronic circuit containing inductance $L$ and capacitance $C$ in series is given by

$f=\frac{1}{2\pi \sqrt{LC}}$

(a) Determine the resonance frequency in an electronic circuit if the inductance is 9 and the capacitance is $0.0001$ . Use $\pi =\mathrm{3.14.}$

(b) Determine the inductance in an electric circuit if the resonance frequency is $5.308$ and the capacitance is $0.0001$ . Use $\pi =\mathrm{3.14.}$

If two magnetic poles of strength $m$ and $m^{\text{'}}$ units are at a distance $r$ centimeters (cm) apart, the force $F$ of repulsion in air between them is given by

$F=\frac{m{m}^{\text{'}}}{r^2}$

(a) Determine the force of repulsion if two magnetic poles of strengths 22 and 46 units are 8 cm apart.

(b) Determine how far apart are two magnetic poles of strengths 14 and 16 units if the force of repulsion in air between them is 42 units.