# How do you simplify (sqrt75-sqrt27)/sqrt12?

Mar 19, 2018

See a solution process below:

#### Explanation:

First, rewrite each of the radicals as:

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

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

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

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

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

$\frac{5 \sqrt{\textcolor{b l u e}{3}} - 3 \sqrt{\textcolor{b l u e}{3}}}{2 \sqrt{\textcolor{b l u e}{3}}}$

Next, factor out the common term in the numerator:

$\frac{\left(5 - 3\right) \sqrt{\textcolor{b l u e}{3}}}{2 \sqrt{\textcolor{b l u e}{3}}} \implies$

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

$1$