How do you divide $(2sqrt108)/sqrt(180y)$ ?

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Answer 1 · 2015-04-01T04:00:27

$(2sqrt(3))/sqrt(5y)$ or $(2sqrt(15y))/(5y)$

$(2sqrt(108))/sqrt(180y)$

We can factor the numbers inside the square root into perfect squares:

$(2sqrt(36 * 3))/sqrt(36*5y)$

Since the square root of $36$ is $6$ :

$(2*6sqrt(3))/(6sqrt(5y))$

Cancel out $6$ from both the numerator and denominator:

$(2sqrt(3))/sqrt(5y)$

It is technically "simplified" here. If you are asked to rationalize the denominator, multiply both the numerator and the denominator by $sqrt(5y)$ :

$((2sqrt(3))/sqrt(5y))*(sqrt(5y))/(sqrt(5y))$

$(2sqrt(15y))/(5y)$

How do you divide (2sqrt108)/sqrt(180y)(2sqrt108)/sqrt(180y)?