# How do you simplify (6 sqrt 5) div (5 sqrt 3)?

Mar 5, 2016

#### Answer:

$\frac{2 \sqrt{15}}{5}$

#### Explanation:

To simplify

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

We should "rationalize" the denominator. This means, try to get the $\sqrt{3}$ out of the denominator.

We can do this by multiplying the fraction by $\frac{\sqrt{3}}{\sqrt{3}}$.

$= \frac{6 \sqrt{5}}{5 \sqrt{3}} \left(\frac{\sqrt{3}}{\sqrt{3}}\right)$

In the numerator, we use the rule that $\sqrt{a} \sqrt{b} = \sqrt{a b}$, so $\sqrt{5} \sqrt{3} = \sqrt{15}$.

In the denominator, we see that $\sqrt{3} \sqrt{3} = 3$, so the square root has been eliminated from the denominator.

$= \frac{6 \sqrt{15}}{5 \cdot 3}$

Simplify the fraction:

$= \frac{2 \sqrt{15}}{5}$