# How do you simplify sqrt3(2sqrt5-3sqrt3)?

Jun 3, 2017

Seea solution process below:

#### Explanation:

First, to eliminate the parenthesis, multiply each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{\sqrt{3}} \left(2 \sqrt{5} - 3 \sqrt{3}\right) \implies$

$\left(\textcolor{red}{\sqrt{3}} \cdot 2 \sqrt{5}\right) - \left(\textcolor{red}{\sqrt{3}} \cdot 3 \sqrt{3}\right) \implies$

$2 \sqrt{3} \sqrt{5} - 3 \sqrt{3} \sqrt{3}$

We can now use this rule for multiplying radicals to simplify the expression:

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

$2 \sqrt{\textcolor{red}{3}} \sqrt{\textcolor{b l u e}{5}} - 3 \sqrt{\textcolor{red}{3}} \sqrt{\textcolor{b l u e}{3}} \implies$

$2 \sqrt{\textcolor{red}{3} \cdot \textcolor{b l u e}{5}} - 3 \sqrt{\textcolor{red}{3} \cdot \textcolor{b l u e}{3}} \implies$

$2 \sqrt{15} - 3 \sqrt{9} \implies$

$2 \sqrt{15} - \left(3 \cdot 3\right) \implies$

$2 \sqrt{15} - 9$