# Roots and Powers of Algebraic Expressions

### Simplifying Square Roots of Powers in Radical Expressions

Simplifying radical expressions that contain powers can be tricky. There are a few simple rules that will help you perform these simplifications with ease. This lesson will teach you how.Find a Partner

### What Do Those Radical Symbols Mean?

The radical symbol looks like this:

√x

and is defined as a number that gives a specified quantity when multiplied to itself. For example, the square root of 25 is 5. 5 is a number that when multiplied to itself gives the specific number 25. This also means that the inverse of the square root is squared. When you square a number, taking its square root brings you back to the original number. The square root of 16 = 4; 4^2 = 16.< /P>

Since the radical symbol is the opposite of squared, we can make the following statement: the square root of x^2 = x.

The same basic rules apply when you are simplifying radicals that contain numbers, except it can be slightly more difficult to break down a number than a variable - Simplify: the square root of 75.

As with variables, first break apart the number, 5 *5 * 3, then find pa

As with variables, first break apart the number, 5 *5 * 3, then find partners, 5^2 * 3. Any number with a partner can be removed from the radical to get your final answer, which is 5 * the square root of 3.

### Lesson Summary

When simplifying radicals containing exponents, you first need to write the terms out, then find each term a partner. If there are not enough of the like terms to give everyone a partner, one can stay single. Then for each partnership, one of the terms gets placed on the outside of the radical. Any single terms will remain under the radical. Lastly, combine any terms outside the radical, if possible. For example, change b * b to b^2.