# How do you simplify sqrt12*sqrt15?

Mar 5, 2018

See a solution process below:

#### Explanation:

First, use this rule for radicals to rewrite the expression as:

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

$\sqrt{\textcolor{red}{12}} \cdot \sqrt{\textcolor{b l u e}{15}} \implies \sqrt{\textcolor{red}{12} \cdot \textcolor{b l u e}{15}} \implies \sqrt{180}$

Next, rewrite the expression as:

$\sqrt{180} \implies \sqrt{36 \cdot 5}$

Now, use the rule above in reverse to complete the simplification:

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

$\sqrt{\textcolor{red}{36} \cdot \textcolor{b l u e}{5}} \implies \sqrt{\textcolor{red}{36}} \cdot \sqrt{\textcolor{b l u e}{5}} \implies 6 \sqrt{5}$