# How do you simplify 7sqrt54-sqrt24?

Apr 27, 2018

See a solution process below:

#### Explanation:

First, we can rewrite the terms under the radicals as:

$7 \sqrt{9 \cdot 6} - \sqrt{4 \cdot 6}$

Next, we can use this rule for radicals to simplify the radical terms:

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

$7 \sqrt{\textcolor{red}{9} \cdot \textcolor{b l u e}{6}} - \sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{6}} \implies$

$7 \sqrt{\textcolor{red}{9}} \sqrt{\textcolor{b l u e}{6}} - \sqrt{\textcolor{red}{4}} \sqrt{\textcolor{b l u e}{6}} \implies$

$\left(7 \cdot 3 \sqrt{\textcolor{b l u e}{6}}\right) - 2 \sqrt{\textcolor{b l u e}{6}} \implies$

$21 \sqrt{\textcolor{b l u e}{6}} - 2 \sqrt{\textcolor{b l u e}{6}}$

Now, we can factor out the common term:

$\left(21 - 2\right) \sqrt{\textcolor{b l u e}{6}} \implies$

$19 \sqrt{\textcolor{b l u e}{6}}$