# How do you simplify sqrt7( sqrt35 + sqrt 7)?

Aug 8, 2017

See a solution process below:

#### Explanation:

First, multiply each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{\sqrt{7}} \left(\sqrt{35} + \sqrt{7}\right) \implies$

$\left(\textcolor{red}{\sqrt{7}} \times \sqrt{35}\right) + \left(\textcolor{red}{\sqrt{7}} \times \sqrt{7}\right) \implies$

$\left(\textcolor{red}{\sqrt{7}} \times \sqrt{35}\right) + 7$

Next, rewrite the term on the left using this rule of radicals:

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

$\left(\textcolor{red}{\sqrt{7}} \times \textcolor{b l u e}{\sqrt{35}}\right) + 7 \implies$

$\sqrt{\textcolor{red}{7} \times \textcolor{b l u e}{35}} + 7 \implies$

$\sqrt{\textcolor{red}{7} \times \textcolor{b l u e}{7 \times 5}} + 7 \implies$

$\sqrt{\textcolor{red}{49} \times \textcolor{b l u e}{5}} + 7 \implies$

$\left(\sqrt{\textcolor{red}{49}} \times \sqrt{\textcolor{b l u e}{5}}\right) + 7 \implies$

$7 \sqrt{\textcolor{b l u e}{5}} + 7$