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

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Answer 1 · 2018-04-10T21:15:04

Let's start by factorizing:

$180=(2xx2)xx(3xx3)xx5$
$540=2xx2xx3xx3xx3xx5$

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

$=(cancel2xxcancel3sqrt(5y))/(cancel2xx2xxcancel3xx3xx3xx5)=sqrt(5y)/90$

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