# Simplify 3sqrt(125/36)?

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

#### Explanation:

I'm reading this as $3 \sqrt{\frac{125}{36}}$

First thing to do is see that we can rewrite the terms under the square root sign into terms that have perfect squares:

$3 \sqrt{\frac{5 \times 25}{36}}$

$3 \left(\frac{\sqrt{5} \times \sqrt{25}}{\sqrt{36}}\right)$

Let's take square roots of the perfect squares:

$3 \times \frac{\sqrt{5} \times 5}{6}$

$\frac{3 \times \sqrt{5} \times 5}{6}$

Let's cancel the 6 in the denominator against the 3 in the numerator and reorder the terms:

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