In the first section, we talked about the importance of simplifying radical expressions, and there's a reason for doing this that we didn't mention then: writing radical expressions in simplest form may allow us to combine terms and simplify an expression even more.

Take the following expression as an example: + +

This expression can be simplified by first simplifying each individual term:

+ + =
+ + = 
2 + 3 + 5

Now, we notice that in each case we have a number multiplied by , so they are essentially like terms or "like radicals," and we can combine them in the same way that we combine like terms.

2 + 3 + 5 = (2 + 3 + 5) = 10.

Of course, we won't always have like radicals when we simplify, but when we do, we can combine them. Here's an example: Simplify the expression + + + .

+ + + = 
+ + + =
+ + 2 + 7

Note that we have two terms with and two terms with . These pairs of terms can be combined:

+ + 2 + 7 = 
(1 + 7) + (1 + 2) = 
8 + 3

The same process will work with variables, and it will also work with cube roots and other radicals. Simplify the following expression: +

When we simplify each of these, we obtain:

2x + 3x = 5x

1.

Simplify +

2.

Simplify +

3.

Simplify + + +

4.

Simplify +

5.

Simplify -