Question

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

Answer 1

`(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)`