2. Adding and Subtracting Radical Expressions
When two radical expressions have the same indices and radicands, they are said to be like radicals. Like radicals can be combined (added or subtracted) in much the same way that we combined like terms earlier in this text.
Example
Simplify by combining like radical terms.

3. Products and Quotients of Two or More Radical Terms
Example
Multiply.
Using the distributive law
In part (c) of the last example, notice that, m – n, is not itself a radical expression. Pairs of radical terms like,
are called conjugates.

4. Rationalize the denominator:
Rationalizing Denominators and Numerators (Part 2)
The use of conjugates allows us to rationalize denominators or numerators with two terms.
Example
Rationalize the denominator:
Solution
Multiplying by clever form of 1 using the conjugate

5. To rationalize a numerator with more than one term, we use the conjugate of the numerator.

6. Terms with Differing Indices
To multiply or divide radical terms with different indices, like
We can convert to exponential notation, use the rules for exponents, and then convert back to radical notation.
Example
Multiply and, if possible, simplify:
Solution
Converting to exponential notation
Adding exponents
Converting to radical notation
Simplifying