You may want to review roots and the laws of exponents first.
The laws of exponents tell us that √(ab) = √a√b. This means, for example, that √6 = √2√3. This is useful if the thing inside the root sign has a factor which is a square. For example, √12 = √4√3 = 2√3. This is considered simpler than √12.
If the thing inside the root sign has a denominator, we can also use this rule. For example, √(2 ⁄ 3) = √(1 ⁄ 9)√6 = (1 ⁄ 3)√6. This is again usually considered simpler, because the root is simpler. (The idea is that, even without a calculator, you could probably look up or guess what √6 comes out to approximately.) You're done when the thing inside the root sign (called the radicand) is a whole number and isn't divisible by any squares bigger than 1.
It works the same way for higher roots, like cube roots or fourth roots. For example, 3√96 = 3√8 3√12 = 2 3√12. We're done because 12 isn't divisible by any cubes.