Simplify 4√6/√30

Question

by rationalizing the denominator. Show your work.

Answer 1

First, we simplify the expressions under the square roots:

√6 = √(2*3) = √2√3
√30 = √(2*3*5) = √2√3√5

Next, we substitute these simplifications back into our original expression:

4√6/√30 = 4(√2√3)/(√2√3√5)

Now, we can simplify by cancelling out the common factors in the numerator and denominator:

= 4(√2√3)/(√2√3√5)
= 4(√2)/(√5)
= (4√2)/(√5)

Therefore, the simplified expression is (4√2)/(√5) after rationalizing the denominator.