# How do you simplify sqrt11 (sqrt6 - sqrt7)?

Nov 14, 2017

See a solution process below:

#### Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{\sqrt{11}} \left(\sqrt{6} - \sqrt{7}\right) \implies$

$\left(\textcolor{red}{\sqrt{11}} \times \sqrt{6}\right) - \left(\textcolor{red}{\sqrt{11}} \times \sqrt{7}\right)$

Now, use this rule for radicals to combine the radicals within the parenthesis:

$\sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}}$

$\left(\sqrt{\textcolor{red}{11}} \cdot \sqrt{\textcolor{b l u e}{6}}\right) - \left(\sqrt{\textcolor{red}{11}} \cdot \sqrt{\textcolor{b l u e}{7}}\right) \implies$

$\sqrt{\textcolor{red}{11} \cdot \textcolor{b l u e}{6}} - \sqrt{\textcolor{red}{11} \cdot \textcolor{b l u e}{7}} \implies$

$\sqrt{66} - \sqrt{77}$