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).