What is the simplest radical form of #3 sqrt(12) / (5sqrt(5))#?

1 Answer
Jul 23, 2015

Answer:

#(6sqrt(15))/25#

Explanation:

There's really not much you can do to the denominator except rationalize it, so focus on the numerator first.

#(3 sqrt(12))/(5sqrt(5)) = (3 sqrt(4 * 3))/(5sqrt(5)) = (3 sqrt(2""^2 * 3))/(5sqrt(5)) = (3 * 2sqrt(3))/(5sqrt(5)) = (6sqrt(3))/(5sqrt(5))#

To rationalize the denominator, multiply the numerator and the denominator by #sqrt(5)#. This will get you

#(6sqrt(3) * sqrt(5))/( 5sqrt(5) * sqrt(5)) = (6sqrt(3 * 5))/(5 * 5) = color(green)((6sqrt(15))/25)#