# How do you simplify (3sqrt20)/(2sqrt4)?

Feb 16, 2017

$\frac{3 \sqrt{5}}{2}$

#### Explanation:

to simplify $\frac{3 \sqrt{20}}{2 \sqrt{4}}$ you need to rationalize the denominator which means you need to get rid of that square root in the denominator

fortunately $\sqrt{4} = 2$ so simplifying this expression is easy

$\frac{3 \sqrt{20}}{2 \sqrt{4}} = \frac{3 \sqrt{20}}{2 \cdot 2} = \frac{3 \sqrt{20}}{4}$

and $\sqrt{20} = 2 \sqrt{5}$

$\frac{3 \sqrt{20}}{4} = \frac{3 \cdot 2 \sqrt{5}}{4} = \frac{6 \sqrt{5}}{4} = \frac{3 \sqrt{5}}{2}$