TEXT: Intermediate Algebra by Miller, O’Neill & Hyde
Videos from a variety of sources, including Khan Academy.
To add or subtract polynomials, we combined like terms. In some sense, we extend the notion of “like” developed with polynomials to radicals.
DEFINITION Like Radicals
Two terms with square roots are called like radicals if they have the same radicand.
To combine like radicals, we factor out the radical (using the distributive property in reverse) . In your homework, you will often have to simplify the radicals before you combine the like radicals. See coolmath or purplemath for detail and examples with just numbers. Some videos with just numbers:
The mathportal has examples, explanation and exercises with numbers as well as with variables. An example with numbers and then one with variables (you may ignore the last example which is with a cube root):
An example with variables: