# What is the square root of 32 over square root of 8?

Mar 21, 2018

See a solution process below:

#### Explanation:

We can rewrite this expression as:

$\frac{\sqrt{32}}{\sqrt{8}} \implies \frac{\sqrt{8 \cdot 4}}{\sqrt{8}}$

Now, we can use this rule for radicals to rewrite the numerator and complete the simplification:

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

$\frac{\sqrt{\textcolor{red}{8} \cdot \textcolor{b l u e}{4}}}{\sqrt{8}} \implies$

$\frac{\sqrt{\textcolor{red}{8}} \cdot \sqrt{\textcolor{b l u e}{4}}}{\sqrt{8}} \implies$

$\frac{\cancel{\sqrt{\textcolor{red}{8}}} \cdot \sqrt{\textcolor{b l u e}{4}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{8}}}}} \implies$

$\sqrt{\textcolor{b l u e}{4}} \implies$

$2$

We can also use this rule of radicals to rewrite and simplify the expression:

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

$\frac{\sqrt{\textcolor{red}{32}}}{\sqrt{\textcolor{b l u e}{8}}} \implies$

$\sqrt{\frac{\textcolor{red}{32}}{\textcolor{b l u e}{8}}} \implies$

$\sqrt{4} \implies$

$2$