# How do you simplify 9sqrt3 - 2sqrt12?

Jun 25, 2018

See a solution process below:

#### Explanation:

First, use this rule for radicals to simplify the radical on the right:

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

$9 \sqrt{3} - 2 \sqrt{12} \implies$

$9 \sqrt{3} - 2 \sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{3}} \implies$

$9 \sqrt{3} - 2 \sqrt{\textcolor{red}{4}} \sqrt{\textcolor{b l u e}{3}} \implies$

$9 \sqrt{3} - \left(2 \cdot 2 \sqrt{\textcolor{b l u e}{3}}\right) \implies$

$9 \sqrt{3} - 4 \sqrt{\textcolor{b l u e}{3}}$

Now, we can factor out the common term giving:

$9 \sqrt{\textcolor{b l u e}{3}} - 4 \sqrt{\textcolor{b l u e}{3}} \implies$

$\left(9 - 4\right) \sqrt{\textcolor{b l u e}{3}} \implies$

$5 \sqrt{3}$