When presented with a problem like , we don’t have too much difficulty saying that the answer 2 (since ). Even a problem like is easy once we realize . Our trouble usually occurs when we either can’t easily see the answer or if the number under our radical sign is not a perfect square or a perfect cube.

A problem like may look difficult because there are no two numbers that multiply together to give 24. However, the problem can be simplified. So even though 24 is not a perfect square, it can be broken down into smaller pieces where one of those pieces might be perfect square. So now we have .

Simplifying a radical expression can also involve variables as well as numbers. Just as you were able to break down a number into its smaller pieces, you can do the same with variables. When the radical is a square root, you should try to have terms raised to an even power (2, 4, 6, 8, etc). When the radical is a cube root, you should try to have terms raised to a power of three (3, 6, 9, 12, etc.). For example,

These types of simplifications with variables will be helpful when doing operations with radical expressions. Let's apply these rule to simplifying the following examples.

#1. Simplify

#2. Simplify

#3. Simplify

#4. Simplify