# How do you simplify: 10x the square root of 8 over the square root of 16?

Jul 24, 2015

=color(green)(5sqrt2

#### Explanation:

Prime factorising $8$:

$\sqrt{8} = \sqrt{2 \cdot 2 \cdot 2}$
$= 2 \sqrt{2}$

• Now 10 times $\sqrt{8}$ :

= 10 xx sqrt8 = 10 xx 2sqrt2 = color(green)(20sqrt2

• Now 10 times $\sqrt{8}$ over $\sqrt{16}$ :

$= \frac{10 \sqrt{8}}{\sqrt{16}}$

$= \frac{\textcolor{g r e e n}{\left(20 \sqrt{2}\right)}}{\sqrt{16}}$

we know sqrt 16=color(green)(4

$= \frac{20 \sqrt{2}}{4}$

=color(green)(5sqrt2