# How do you simplify sqrt(32/4)?

Jan 29, 2016

$2 \sqrt{2}$

#### Explanation:

There are 2 solutions :)

The first solution is:

Since $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$, where $b$ is not equal to $0$.

First we simplify the numerator, since there is no exact value of $\sqrt{32}$ we take its perfect squares. $16$ is a perfect square since $4 \cdot 4 = 16$. Dividing $32$ by $16$, we get $16 \cdot 2 = 32$, therefore:

$\sqrt{32} = \sqrt{16} \cdot \sqrt{2}$
$= 4 \sqrt{2}$

Since now we're done in the numerator, we're gonna simplify the denominator, since $4$ is perfect square, $4 = 2 \cdot 2$, the $\sqrt{4}$ is equal to $2$.

Plugging all the answers, we get:

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

since $4$ and $2$ is a whole number, we can divide these 2 whole numbers, we get:

$2 \sqrt{2}$

this is the final answer :)

the 2nd solution is:

First we simply evaluate the fraction inside the radical sign (square root)

$\sqrt{\frac{32}{4}} = \sqrt{8}$

since, $\frac{32}{4}$ = $8$, then we get $\sqrt{8}$

$\sqrt{8} = \sqrt{4} \cdot \sqrt{2}$

$= 2 \sqrt{2}$