# How do you simplify sqrt16/sqrt8?

Apr 26, 2018

=$\sqrt{2}$

#### Explanation:

$\frac{\sqrt{16}}{\sqrt{8}}$ Multiply the fraction by $1$ as $\frac{\sqrt{8}}{\sqrt{8}}$:
=$\frac{\sqrt{16 \cdot 8}}{8}$ Factor $16$ and $8$:
=$\sqrt{\left(2 \cdot 2 \cdot 2 \cdot 2\right)} \cdot \left(2 \cdot 2 \cdot 2\right)$ Factor out the three pairs of twos:
=$8 \frac{\sqrt{2}}{8}$
=$\sqrt{2}$

OR, if you want to do it the simple way:
$\frac{\sqrt{16}}{\sqrt{8}}$
=$\sqrt{\frac{16}{8}}$
=$\sqrt{2}$
Sorry, forgot you could divide them xD ^^

Apr 26, 2018

$\sqrt{2}$

#### Explanation:

Simplify the square roots

$\frac{\sqrt{16}}{\sqrt{8}}$ = $\frac{4}{\sqrt{4} \sqrt{2}}$ = $\frac{4}{2 \sqrt{2}}$

Rearrange the equation so there is no square root in the denominator

$\frac{4}{2 \sqrt{2}}$$\frac{\sqrt{2}}{\sqrt{2}}$ = (4sqrt2)/(2⋅2) = $\frac{4 \sqrt{2}}{4}$

The fours cancel out and you are left with $\sqrt{2}$