Simplify 4√6/√30 by rationalizing the denominator. Show your work
To simplify 4√6/√30 by rationalizing the denominator, we first need to simplify the radicals.
√6 = √(2*3) = √2√3
√30 = √(2*3*5) = √2√3√5
Now we substitute these simplifications back into the original expression:
4(√2√3) / (√2√3√5)
= 4√2√3 / √2√3√5
= 4√6 / √30
To rationalize the denominator, we multiply the numerator and the denominator by √30:
(4√6 / √30) * (√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 simplified by rationalizing the denominator is 4√5 / 5.