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

Answer 1

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.