You can only add square roots (or radicals) that have the same radicand. So in the example above you can add the first and the
last terms :

The same rule goes for subtracting. Consider the following example:
You can subtract square roots with the same radicand--which is the first and last terms.

Practice Problems

Directions: Add the square roots below

Problem 1

Answer

Only the first and last square root have the same radicand, so you can add these two terms.

Problem 2

Answer

Remember--the same rule applies to subtracting square roots--the radicands must be the same.

Let's look at the following example
. You may immediately see the problem here: The radicands are not the same. Therefore, we can not add them at the moment. However, if we simplify the square roots first, we will be able to add them. Let's use this example problem to illustrate the general steps for adding square roots.

Do you see what distinguishes this expression from the last several problems?

Each square root has a coefficent. The rules for adding square roots with coefficients are very similar to what we just practiced in the last several problems--with 1 additional step --which is to multiply the coefficeints with the simplified square root.

Step 1) Ignore the coefficients ( 2 and 5) and simplify each square root.

Step 2) Multiply the coefficients (2 and 5) by any numbers that 'got out' of the square root (3 and 2, respectively).