# How do you simplify  sqrt108 + 5sqrt3?

Mar 6, 2018

See a solution process below:

#### Explanation:

First we can rewrite the radical on the left as:

$\sqrt{36 \cdot 3} + 5 \sqrt{3}$

We can then use this rule for radicals to simplify the radical on the left:

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

$\sqrt{\textcolor{red}{36} \cdot \textcolor{b l u e}{3}} + 5 \sqrt{3} \implies$

$\left(\sqrt{\textcolor{red}{36}} \cdot \sqrt{\textcolor{b l u e}{3}}\right) + 5 \sqrt{3} \implies$

$6 \sqrt{3} + 5 \sqrt{3}$

We can now factor the common term and complete the simplification:

$\left(6 + 5\right) \sqrt{3} \implies$

$11 \sqrt{3}$