# What is the square root of 12 times the square root of 3?

Sep 11, 2015

(Assuming only principal [non-negative] square roots
$\sqrt{12} \times \sqrt{3} = 6$

#### Explanation:

$\sqrt{12} = \sqrt{{2}^{2} \times 3} = \sqrt{{2}^{2}} \times \sqrt{3} = 2 \sqrt{3}$

So $\sqrt{12} \times \sqrt{3}$
$\textcolor{w h i t e}{\text{XXX}} = 2 \sqrt{3} \times \sqrt{3}$

color(white)("XXX")=(2xx sqrt(3))xxsqrt(3))

$\textcolor{w h i t e}{\text{XXX}} = 2 \times \left(\sqrt{3} \times \sqrt{3}\right)$

$\textcolor{w h i t e}{\text{XXX}} = 2 \times 3$

$\textcolor{w h i t e}{\text{XXX}} = 6$