# How do you simplify 3sqrt15 * 5sqrt35?

May 18, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$3 \cdot 5 \cdot \sqrt{15} \cdot \sqrt{35} \implies$

$15 \cdot \sqrt{15} \cdot \sqrt{35}$

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

$15 \cdot \sqrt{\textcolor{red}{15}} \cdot \sqrt{\textcolor{b l u e}{35}} \implies$

$15 \cdot \sqrt{\textcolor{red}{15} \cdot \textcolor{b l u e}{35}} \implies$

$15 \cdot \sqrt{525}$

Then, rewrite the term under the radical as:

$15 \cdot \sqrt{\textcolor{red}{25} \cdot \textcolor{b l u e}{21}} \implies$

$15 \cdot \sqrt{\textcolor{red}{25}} \cdot \sqrt{\textcolor{b l u e}{21}} \implies$

$15 \cdot 5 \cdot \sqrt{\textcolor{b l u e}{21}} \implies$

$75 \sqrt{21}$