# How do you simplify 5 square root 10 times 2 square root 8?

Sep 21, 2015

$40 \sqrt{5}$

#### Explanation:

Because these two radicals have the same index 2, you can easily multiply them.
$5 \sqrt{10} \cdot 2 \sqrt{8}$
$= \left(5\right) \left(2\right) \sqrt{10 \cdot 8}$
$= 10 \sqrt{10 \cdot 8}$
(We will factor 10 and 8)
$= 10 \sqrt{\left(5 \cdot 2\right) \cdot \left(2 \cdot 2 \cdot 2\right)}$
$= 10 \sqrt{5 \cdot {2}^{4}}$
(${2}^{4}$ is the square of ${2}^{2}$, so we can take that out of the square root symbol now)
$= 10 \left({2}^{2}\right) \sqrt{5}$
$= 10 \left(4\right) \sqrt{5}$
$= 40 \sqrt{5}$