Radicals With Like Terms

• Recall that you can add two expressions if they are like terms.

5 7x x

This process is based on the distributive property, which was shown in the second step.

• Example 1

5 7 x 12x

• In the same way we add two radical expressions if they are like terms.

5 7x x

These terms were like since both radicals had the same index (2 in this case), and the same radicand.

• Example 2

5 7 x 12 x

You are encouraged to leave out the middle step.

• Example 3

Simplify: 2 2 24 4 45 3 12 3 3x x x

Note that all three radicals have the same index …

… and the same radicand.

Add and subtract the coefficients to get …

245 12 1 3x 246 3x

• Sometimes it is necessary to simplify the radicals first in order to create like terms.

4 2 2 23 32 24 9 3x x y x xy

• Example 4

Simplify:

3 2 2 23 32 8 3 9 3x x x y x xy

3 2 2 23 32 8 3 9 3x x x y x xy

3 3 2 2 23 32 8 3 9 3x x x y x xy

2 2 23 32 2 3 9 3x x x y x xy

2 2 2 23 34 3 9 3x xy x xy

2 235 3x xy

Like Terms