Multiply the numerator (top) and denominator (bottom) of the fraction by the denominator if the denominator contains a radical sign. For example, if you have 4/√5, you would multiply the top and bottom of the fraction by √5 to get 4√5/5. Multiplying the radical times itself in the denominator leaves you with just the radicand and no radical sign.
Simplify the fraction if the entire fraction is covered by the radical sign, or the numerator and denominator each have a radical sign. For example, √20/√5 = √4, which equals 2.
Extract any perfect squares or cubes (or greater) if present with a radical in a fraction. For example, if you have √64/11, you would extract 8 since 8 times 8 equals 64. This would give you an answer of 8/11. Another example would be ^3√8/5. The cube root of 8 is 2, so the answer would be 2/5.
Simplify fractional parts outside of the radical sign if necessary. For example, if you have 12√2/√9, you would first rewrite the fraction as 12√2/3. Then 3 divides into 12 four times leaving you with 4√2.