# How do you simplify -sqrt12+3sqrt3?

May 30, 2017

See a solution process below:

#### Explanation:

We can use this rule of radicals to rewrite the radical on the left of the expression:

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

$- \sqrt{12} + 3 \sqrt{3} \implies - \sqrt{4 \cdot 3} + 3 \sqrt{3} \implies - \left(\sqrt{4} \cdot \sqrt{3}\right) + 3 \sqrt{3} \implies - 2 \sqrt{3} + 3 \sqrt{3}$

We can now combine like terms. In this case the $\sqrt{3}$ term is the like term:

$- 2 \sqrt{3} + 3 \sqrt{3} \implies \left(- 2 + 3\right) \sqrt{3} \implies - 1 \sqrt{3} \implies$

$- \sqrt{3}$