Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify 46√30√ by rationalizing the denominator. Show your work.
To simplify 46√30, we need to find the prime factorization of 30 first.
30 = 2 * 3 * 5
Now, we can simplify 46√30 by factoring out the perfect square within the square root:
46√30 = 46√(2 * 3 * 5) = 46√(2 * 3 * 5) = 46√(6 * 5) = 46√(30) = 46√(2 * 3 * 5) = 46√(2) * √(3) * √(5) = 46√5√3√2 = 46√15√2
Therefore, 46√30 is equivalent to 46√15√2.