Simplify 4√6/√30 by rationalizing the denominator. Show your work.

To simplify 4√6/√30, we first need to rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator:

4√6/√30 * √30/√30
= 4√6*√30 / 30
= 4√(6*30) / 30
= 4√180 / 30
= 4(√36 * √5) / 30
= 4(6√5) / 30
= 24√5 / 30
= 12√5 / 15
= 4√5 / 5

Therefore, 4√6/√30 simplifies to 4√5/5.