In this Section:
In this section, we learn how to add and subtract radicals. We begin by learning about “like radicals”. Like radicals have the same index and the same radicand. This is similar to when we learned about “like terms” at the beginning of algebra. Recall that like terms have the same variable, raised to the same power. When we have like radicals, the process of addition or subtraction is simple. We add or subtract the numbers multiplying the radicals, and leave the common radical unchanged. An easy way to see this is by factoring out the common radical. This will allow one to visualize why we only perform operations with the numbers multiplying the radicals. We will encounter many problems that appear to not have like radicals. These problems commonly require us to simplify each radical first, then attempt to find like radicals. In many cases, we will have like radicals that can be combined with addition or subtraction. Once we are done, we must remember to simplify all radicals before we report our answer.