# What is the square root of 4/125?

Oct 9, 2015

$\sqrt{\frac{4}{125}} = \frac{2 \sqrt{5}}{25}$

#### Explanation:

$\sqrt{\frac{4}{125}}$

Simplify.

$\frac{\sqrt{4}}{\sqrt{125}}$

Determine the prime factors for $4$ and $125$.

$\frac{\sqrt{2 \times 2}}{\sqrt{5 \times 5 \times 5}}$

(sqrt(2^2))/(sqrt(5^2xx5)

Apply square root rule $\sqrt{{a}^{2}} = a$.

$\frac{2}{5 \sqrt{5}}$

Rationalize the denominator.

$\frac{2}{5 \sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} =$

$\frac{2 \sqrt{5}}{5 \sqrt{5} \sqrt{5}} =$

Simplify $\sqrt{5} \sqrt{5}$ to $5$.

$\frac{2 \sqrt{5}}{5 \times 5} =$

$\frac{2 \sqrt{5}}{25}$