How do you simplify sqrt12 / sqrt5?

2 Answers
smendyka
Jul 15, 2017

See a solution process below:

Explanation:

First, we can rationalize the denominator by multiplying the the fraction by the appropriate form of 1:

sqrt(5)/sqrt(5) * sqrt(12)/sqrt(5) =>

(sqrt(5) * sqrt(12))/(sqrt(5) * sqrt(5)) =>

sqrt(5 * 12)/5 =>

sqrt(60)/5

Next, we can simplify the numerator as follows:

sqrt(60)/5 =>

sqrt(4 * 15)/5 =>

(sqrt(4) * sqrt(15))/5 =>

(2sqrt(15))/5

Fleur
Jul 15, 2017

(2sqrt15)/5

Explanation:

First, multiply the numerator and denominator by sqrt5, which will get rid of the radical in the denominator. This is essentially the same as multiplying the expression by 1.

sqrt12/sqrt5 * color(blue)(sqrt5/sqrt5)

sqrt5 * sqrt 5 = sqrt25 = 5, so the denominator becomes 5. Similarly, sqrt12 * sqrt 5 = sqrt60.

=sqrt60/5

Now, we can split sqrt60 into sqrt4*sqrt15.

=(sqrt4*sqrt15)/5

=(2sqrt15)/5

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