# How do you rationalize the denominator and simplify (-24sqrt45)/(72sqrt20)?

Aug 5, 2017

$- \frac{1}{2}$

#### Explanation:

First, simplify as much as possible:

(-24sqrt45)/(72sqrt20

$\frac{24}{72} = \frac{1}{3}$, so

(-sqrt45)/(3sqrt20

Simplify the radicals as much as possible:

$45 = 3 \cdot 3 \cdot 5$
$\sqrt{45} = 3 \sqrt{5}$

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

Replace:

(-3sqrt5)/(3*2sqrt5

Simplify:

-(1)/(2