91Ó°ÊÓ

In the following exercises, multiply.

$$\begin{gathered} {a)(4+\sqrt{11})}^2 \\ b){\left(3-2\sqrt{5}\right)}^2 \end{gathered}$$

In the following exercises, multiply.

$\left(7+\sqrt{10}\right)\left(7-\sqrt{10}\right)$

In the following exercises, multiply.

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

Explain what is meant by the $n^{th}$ root of a number.

In the following exercises, simplify

$$\begin{gathered} a\left)\frac{\sqrt{48}}{\sqrt{75}} \\ b\right)\frac{\sqrt[3]{81}}{\sqrt[3]{24}} \end{gathered}$$

In the following exercises, simplify.

$$\begin{gathered} a)\frac{\sqrt{320m{n}^{-5}}}{\sqrt{45m^{-7}{n}^3}} \\ b)\frac{\sqrt[3]{16x^4{y}^{-2}}}{\sqrt[3]{-54x^{-2}{y}^4}} \end{gathered}$$

In the following exercises, rationalize the denominator.

$$\begin{gathered} a)\frac{8}{\sqrt{3}} \\ b)\sqrt{\frac{7}{40}} \\ c)\frac{8}{\sqrt{2y}} \end{gathered}$$

In the following exercises, rationalize the denominator.

$$\begin{gathered} a)\frac{1}{\sqrt[3]{11}} \\ b)\sqrt[3]{\frac{7}{54}} \\ c)\frac{3}{\sqrt[3]{3x^2}} \end{gathered}$$

In the following exercises, rationalize the denominator.

$$\begin{gathered} a)\frac{1}{\sqrt[4]{4}} \\ b)\sqrt[4]{\frac{9}{32}} \\ c)\frac{6}{\sqrt[4]{9x^3}} \end{gathered}$$

In the following exercises, simplify.

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