# How do you simplify the expression sqrt96 div sqrt8?

May 22, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\frac{\sqrt{96}}{\sqrt{8}}$

Next, use this rule for radicals to start the simplification:

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

$\frac{\sqrt{\textcolor{red}{96}}}{\sqrt{\textcolor{b l u e}{8}}} \implies \sqrt{\frac{\textcolor{red}{96}}{\textcolor{b l u e}{8}}} \implies \sqrt{12}$

Then, rewrite the term under the radical as:

$\sqrt{4 \cdot 3}$

Now, use this rule for radicals to complete the simplification:

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

$\sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{3}} \implies \sqrt{\textcolor{red}{4}} \cdot \sqrt{\textcolor{b l u e}{3}} \implies 2 \sqrt{3}$