Simplify (4\sqrt(6))/(\sqrt(30)) by rationalizing the denominator. Show your work.

Answer 1

To simplify (4√6)/(√30), we need to rationalize the denominator by multiplying both the numerator and denominator by √30:

(4√6)(√30) / (√30)(√30)
= 4√(6*30) / √900
= 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.