# How do you find the simplest radical form of 12?

Mar 25, 2018

The simplified radical form of $\sqrt{12}$ is $2 \sqrt{3}$.

#### Explanation:

We need to utilize these two radical rules:

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

$\textcolor{red}{\sqrt{{\textcolor{b l a c k}{a}}^{2}}} = a$

To solve our problem, first, factor $12$ into its prime factorization, then apply those two rules. Here's what that will look like:

$\textcolor{w h i t e}{=} \sqrt{12}$

$= \sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{3}}$

$= \sqrt{\textcolor{red}{2 \cdot 2} \cdot \textcolor{b l u e}{3}}$

$= \sqrt{\textcolor{red}{{2}^{2}} \cdot \textcolor{b l u e}{3}}$

$= \sqrt{\textcolor{red}{{2}^{2}}} \cdot \sqrt{\textcolor{b l u e}{3}}$

$= \textcolor{red}{2} \cdot \sqrt{\textcolor{b l u e}{3}}$

$= \textcolor{red}{2} \sqrt{\textcolor{b l u e}{3}}$

That's as simplified as it gets. Hope this helped!