How do you simplify sqrt12 times sqrt 6?

Mar 4, 2016

$6 \sqrt{2}$

Explanation:

To simplify $\sqrt{12} \times \sqrt{6}$, first let us factorize each of the numbers

$\sqrt{12} \times \sqrt{6}$ = $\sqrt{2 \times 2 \times 3} \times \sqrt{2 \times 3}$

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

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

=$6 \sqrt{2}$

Mar 4, 2016

$\sqrt{12} \times \sqrt{6} = \textcolor{b l u e}{6 \sqrt{2}}$

Explanation:

$\sqrt{12} \times \sqrt{6}$

Simplify $\sqrt{12}$.

$\sqrt{12} = \left(2 \times 2 \times 3\right)$

$\sqrt{12} = \left({2}^{2} \times 3\right)$

Apply square root rule ${\sqrt{a}}^{2} = a$.

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

Rewrite the expression.

$2 \sqrt{3} \times \sqrt{6} =$

$2 \sqrt{18}$

Simplify $2 \sqrt{18}$.

$2 \sqrt{18} = 2 \sqrt{2 \times 3 \times 3}$

$2 \sqrt{18} = 2 \sqrt{2 \times {3}^{2}}$

Apply square root rule ${\sqrt{a}}^{2} = a$.

$2 \sqrt{18} = 2 \times 3 \sqrt{2}$

$2 \sqrt{18} = 6 \sqrt{2}$