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

Answer 1

To simplify the expression 4√6/√30, we first need to rationalize the denominator by multiplying both the numerator and denominator by √30.

(4√6/√30) * (√30/√30)
= 4√(6*30)/30
= 4√180/30
= 4√(2*2*3*3*5)/30
= 4*2*3√5/30
= 24√5/30
= 12√5/15
= 4√5/5

Therefore, the simplified form of 4√6/√30 is 4√5/5.