9.9 Proficiency exam

( [link] ) $\sqrt{8}·\sqrt{5}$

( [link] ) $\frac{\sqrt{80}}{\sqrt{12}}$

( [link] , [link] ) $\frac{\sqrt{n^2+n-12}}{\sqrt{n-3}}$

( [link] , [link] ) $\sqrt{24a^3{b}^5{c}^8}$

( [link] , [link] ) $\sqrt{\frac{64x^4{y}^5{z}^6}{49a^3{b}^2{c}^9}}$

( [link] ) $\sqrt{{\left(x-2\right)}^2{\left(x+1\right)}^4}$

( [link] ) $\sqrt{a^2-8a+16}$

( [link] ) $\frac{4}{2+\sqrt{x}}$

( [link] $\frac{\sqrt{3a}}{\sqrt{2a}+\sqrt{5a}}$

( [link] $2x\sqrt{27}+x\sqrt{12}$

( [link] ) $-3a\sqrt{a^5{b}^3}+2a^{3}b\sqrt{ab}$

( [link] , [link] ) $\sqrt{10}\left(\sqrt{8}-\sqrt{2}\right)$

( [link] , [link] ) $\left(3+\sqrt{6}\right)\left(2+\sqrt{5}\right)$

( [link] , [link] ) $\left(\sqrt{10}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{2}\right)$

( [link] , [link] ) ${\left(4-\sqrt{5y}\right)}^2$

( [link] , [link] ) $\frac{6-\sqrt{3}}{4+\sqrt{2}}$

( [link] , [link] ) $\frac{\sqrt{2}+\sqrt{3}}{\sqrt{3}-\sqrt{5}}$

( [link] ) $\sqrt{x+8}=4$

( [link] ) $\sqrt{3a+1}=4$

( [link] ) $\sqrt{2x}=-3$

( [link] ) $\sqrt{3x+18}+7=0$

( [link] ) $\sqrt{3m-5}=\sqrt{2m+1}$

( [link] ) $2\sqrt{a+2}-2=0$

( [link] ) $\sqrt{b-7}-\sqrt{5b+1}=0$

( [link] ) At a small business, the number of monthly sales $S$ is approximately related to the number of employees $E$ by $S=175+7\sqrt{E-3}.$

(a) Determine the approximate number of sales if the number of employees is 39.
(b) Determine the approximate number of employees if the number of sales is 224.