# How do you simplify 4sqrt27-sqrt75?

Mar 14, 2018

See a solution process below:

#### Explanation:

First, rewrite the two radicals as:

$4 \sqrt{9 \cdot 3} - \sqrt{25 \cdot 3}$

We can now use this rule for radicals to simplify the radicals:

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

$4 \sqrt{\textcolor{red}{9} \cdot \textcolor{b l u e}{3}} - \sqrt{\textcolor{red}{25} \cdot \textcolor{b l u e}{3}} \implies$

$4 \sqrt{\textcolor{red}{9}} \sqrt{\textcolor{b l u e}{3}} - \sqrt{\textcolor{red}{25}} \sqrt{\textcolor{b l u e}{3}} \implies$

$\left(4 \cdot 3 \sqrt{\textcolor{b l u e}{3}}\right) - 5 \sqrt{\textcolor{b l u e}{3}} \implies$

$12 \sqrt{\textcolor{b l u e}{3}} - 5 \sqrt{\textcolor{b l u e}{3}}$

Now, combine the like terms:

$\left(12 - 5\right) \sqrt{\textcolor{b l u e}{3}} \implies$

$7 \sqrt{\textcolor{b l u e}{3}}$