Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify 4√6/30√ by rationalizing the denominator. Show your work.
To simplify the expression 4√6/30√, we first need to rationalize the denominator.
Step 1: Simplify the numerator:
4√6 = √24 = √(4*6) = 2√6
Step 2: Simplify the denominator:
30√ = √900 = √(30*30) = 30
Step 3: Rewrite the expression with the simplified numerator and denominator:
2√6/30
Step 4: Divide both the numerator and denominator by 2 to simplify further:
(2/2)√6/(30/2) = √6/15
Therefore, the simplified form of 4√6/30√ is √6/15.