# How do you simplify 9 sqrt 2 (2 sqrt 7 + 5 sqrt 5)?

Mar 15, 2016

$18 \sqrt{14} + 45 \sqrt{10}$

#### Explanation:

$1$. Distribute the $\textcolor{b l u e}{9} \textcolor{red}{\sqrt{2}}$ to each term within the brackets.

$\textcolor{red}{9} \textcolor{b l u e}{\sqrt{2}} \left(\textcolor{\mathmr{and} a n \ge}{2} \textcolor{p u r p \le}{\sqrt{7}} + \textcolor{t e a l}{5} \textcolor{b r o w n}{\sqrt{5}}\right)$

$= \left(\textcolor{red}{9} \times \textcolor{\mathmr{and} a n \ge}{2}\right) \sqrt{\textcolor{b l u e}{2} \times \textcolor{p u r p \le}{7}} + \left(\textcolor{red}{9} \times \textcolor{t e a l}{5}\right) \sqrt{\textcolor{b l u e}{2} \times \textcolor{b r o w n}{5}}$

$2$. Simplify.

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} 18 \sqrt{14} + 45 \sqrt{10} \textcolor{w h i t e}{\frac{a}{a}} |}}}$