# How do you simplify 10 square root 6 times square root 2?

Sep 8, 2015

By using
$\sqrt{a} \times \sqrt{b} = \sqrt{a b}$,

$10 \sqrt{6} \times \sqrt{2} = 20 \sqrt{3}$

#### Explanation:

To simplify $10 \sqrt{6} \times \sqrt{2}$ we just need to keep in mind the following rule regarding radicals:

$\sqrt{a} \times \sqrt{b} = \sqrt{a b}$

This means that:

$10 \sqrt{6} \times \sqrt{2}$
= 10sqrt(6*2
$10 \sqrt{12}$

From this step, we need to check if we can factor out any perfect squares from $12$. If there is a perfect square, we can factor it out to simplify it more.

$4$ is a perfect square, and we can factor out $4$ from $12$ since $12 = 4 \times 3$. We just apply the rule in reverse, splitting the radical.

$10 \sqrt{12}$
$= 10 \sqrt{4 \times 3}$
$= 10 \sqrt{4} \times \sqrt{3}$
$= 10 \times 2 \times \sqrt{3}$
$= 20 \sqrt{3}$