# How do you simplify sqrt20 + sqrt45?

Mar 20, 2018

See a solution process below:

#### Explanation:

First, rewrite the term under each radical as:

$\sqrt{4 \cdot 5} + \sqrt{9 \cdot 5}$

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

$\sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{5}} + \sqrt{\textcolor{red}{9} \cdot \textcolor{b l u e}{5}} \implies$

$\sqrt{\textcolor{red}{4}} \sqrt{\textcolor{b l u e}{5}} + \sqrt{\textcolor{red}{9}} \sqrt{\textcolor{b l u e}{5}} \implies$

$\textcolor{red}{2} \sqrt{\textcolor{b l u e}{5}} + \textcolor{red}{3} \sqrt{\textcolor{b l u e}{5}}$

Now, factor out the common term to complete the simplification:

$\left(\textcolor{red}{2} + \textcolor{red}{3}\right) \sqrt{\textcolor{b l u e}{5}} \implies$

$\textcolor{red}{5} \sqrt{\textcolor{b l u e}{5}}$