# How do you simplify sqrt12-sqrt75?

Mar 9, 2018

See a solution process below"

#### Explanation:

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

Next, use this rule for exponents to rewrite and simplify each radical:

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

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

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

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

Now, factor out the common term:

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

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