# How do you simplify -2sqrt3+3sqrt27?

Jul 7, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$- 2 \sqrt{3} + 3 \sqrt{9 \cdot 3}$

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

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

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

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

$- 2 \sqrt{3} + 9 \sqrt{3}$

Now, we can factor our the common term giving:

$\left(- 2 + 9\right) \sqrt{3} \implies$

$7 \sqrt{3}$