Question

How do you rationalize `(4sqrt6)/(sqrt30)`?

Answer 1

First note that `sqrt(30) = sqrt(5*6) = sqrt(5)*sqrt(6)`

So `(4sqrt(6))/sqrt(30) = (4sqrt(6))/(sqrt(5)sqrt(6)) = 4/sqrt(5)`

Then rationalize the denominator by multiplying both numerator and denominator by `sqrt(5)`

`4/sqrt(5) = (4sqrt(5))/(sqrt(5)sqrt(5)) = (4sqrt(5))/5`