# How do you rationalize (2sqrt(180y))/540?

Apr 10, 2018

Let's start by factorizing:

#### Explanation:

$180 = \left(2 \times 2\right) \times \left(3 \times 3\right) \times 5$
$540 = 2 \times 2 \times 3 \times 3 \times 3 \times 5$

We may now take all the 'doubles' out from under the root:

$= \frac{\cancel{2} \times \cancel{3} \sqrt{5 y}}{\cancel{2} \times 2 \times \cancel{3} \times 3 \times 3 \times 5} = \frac{\sqrt{5 y}}{90}$