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

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Answer 1 · 2015-07-23T22:48:33

$(6sqrt(15))/25$

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

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

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