# How do you simplify 3sqrt24-sqrt54+sqrt6?

Aug 2, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$3 \sqrt{4 \cdot 6} - \sqrt{9 \cdot 6} + \sqrt{6}$

Use this rule for radicals to simplify the individual terms:

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

$3 \sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{6}} - \sqrt{\textcolor{red}{9} \cdot \textcolor{b l u e}{6}} + \sqrt{6} \implies$

$3 \sqrt{\textcolor{red}{4}} \sqrt{\textcolor{b l u e}{6}} - \sqrt{\textcolor{red}{9}} \sqrt{\textcolor{b l u e}{6}} + \sqrt{6} \implies$

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

We can now factor out the common factor in each term and combine the remainders:

$6 \sqrt{6} - 3 \sqrt{6} + 1 \sqrt{6} \implies$

$\left(6 - 3 + 1\right) \sqrt{6} \implies$

$4 \sqrt{6}$