Math 101 Intermediate Algebra

Adding and Subtracting Radicals
Chapter 8, Section 5

Remember that for the rest of this chapter, it will be assumed that all variables represent non-negative real numbers. So, for example

 =  a, a    0.

Add and Subtract Radicals by Combining Like Radicals

What Are Like Radicals?

Like radicals are radicals having the same radicand and index.

What Are Unlike Radicals?

Unlike radicals are radicals differing in either the radicand or index.

Radicand and index are defined in section 1 of this chapter.

Steps To Add and Subtract Radicals

  1. Simplify each radical expression using the techniques shown in section 3 and section 4 of this chapter.

  2. Combine like radicals, if there are any.

You are done simplifying when all of the following are true:

  1. No perfect powers are factors of any radicand.
  2. No radicand contains a fraction.
  3. No denominator contains a radical.
  4. All like radicals have been combined.