# How do you simplify sqrt (12) - sqrt (27)?

Mar 8, 2018

See a solution process below:

#### Explanation:

First, rewrite the expressions in the radicals as:

$\sqrt{4 \cdot 3} - \sqrt{9 \cdot 3}$

Next, use this rule for radicals to simplify each of the radicals:

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

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

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

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

Now, filter out the common term to complete the simplification:

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

$- 1 \sqrt{\textcolor{b l u e}{3}} \implies$

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