# What is the square root of x^12?

Sep 11, 2015

$\sqrt{{x}^{12}} = {x}^{6}$ (or possibly $- {x}^{6}$ if you want to include the non-principal square root)

#### Explanation:

In general ${\left({b}^{a}\right)}^{c} = {b}^{c a}$

So ${\left({x}^{6}\right)}^{2} = {x}^{2 \times 6} = {x}^{12}$
or reversed
${x}^{12} = {\left({x}^{6}\right)}^{2}$

Therefore
$\sqrt{{x}^{12}} = \sqrt{{\left({x}^{6}\right)}^{2}} = {x}^{6}$