# What is the simplest radical form of 3 sqrt(12) / (5sqrt(5))?

Jul 23, 2015

$\frac{6 \sqrt{15}}{25}$

#### Explanation:

There's really not much you can do to the denominator except rationalize it, so focus on the numerator first.

(3 sqrt(12))/(5sqrt(5)) = (3 sqrt(4 * 3))/(5sqrt(5)) = (3 sqrt(2""^2 * 3))/(5sqrt(5)) = (3 * 2sqrt(3))/(5sqrt(5)) = (6sqrt(3))/(5sqrt(5))

To rationalize the denominator, multiply the numerator and the denominator by $\sqrt{5}$. This will get you

$\frac{6 \sqrt{3} \cdot \sqrt{5}}{5 \sqrt{5} \cdot \sqrt{5}} = \frac{6 \sqrt{3 \cdot 5}}{5 \cdot 5} = \textcolor{g r e e n}{\frac{6 \sqrt{15}}{25}}$