Simplifying Radicals with Fractions

Depending on the problem you have to simplify the numerator and then the denominator. If the denominator is irrational and has a radical you have to rationalize it which is multiplying it by the lowest number that will give you a perfect square. Then simplify.
Example: the square root of 81 over 3. Separate the numerator and the denominator and you get 9 over radical 3 because 81 is a perfect square and 3 is not. Since radical 3 is irrational you rationalize the denominator by multiplying the numerator and the denominator by radical 3. You get 9 radical 3 over radical 9 which can be simplified to 3. 9 and 3 are rational numbers so they can be simplified. Your final answer is 3 radical 3.