Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify 4 square root 6/ sqaure root 30 by rationalizing the denominator. Show your work.
To simplify 4√6/√30, we need to rationalize the denominator.
First, let's break down the square roots:
√6 = √(2*3) = √2 * √3 = √2√3
√30 = √(2*15) = √2 * √15 = √2√15
Now we can rewrite the expression:
4√6/√30 = 4(√2√3)/(√2√15)
= 4√2√3/√2√15
= 4√6/√30
Since we have the same terms in the numerator and denominator, we can simplify further:
4/√5
Therefore, 4√6/√30 simplified by rationalizing the denominator is 4/√5.