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