# How do you simplify 6 sqrt3 - 2 sqrt 12?

Mar 21, 2018

See a solution process below:

#### Explanation:

First, rewrite the term under the radical on the right as:

$6 \sqrt{3} - 2 \sqrt{4 \cdot 3}$

Next, use this rule for radicals to simplify the term on the right:

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

$6 \sqrt{3} - 2 \sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{3}} \implies$

$6 \sqrt{3} - 2 \sqrt{\textcolor{red}{4}} \sqrt{\textcolor{b l u e}{3}} \implies$

$6 \sqrt{3} - \left(2 \cdot 2\right) \sqrt{3} \implies$

$6 \sqrt{3} - 4 \sqrt{3}$

Now, we can factor out the common term to complete the simplification:

$\left(6 - 4\right) \sqrt{3} \implies$

$2 \sqrt{3}$