Section 10.5 Expressions Containing Several Radical Terms

Definition Like Radicals are radicals that have the same index and same radicand.  We can ONLY combine Like Radicals. 1) Simplify each radical. 2) Combine like radicals. To add/subtract radical expressions, we

Solution Simplify by combining like radical terms. Example

Solution Simplify by combining like radical terms. Example

Examples Simplify the following expressions

Product of two or more radical terms 1. Use distributive law or FOIL 2. Use product rule for radicals 3. Simplify and combine like terms. Examples: Multiply. Simplify if possible. Assume all variables are positive

Solution Using the distributive law F O I L

Solution F O I L Notice that the two middle terms are opposites, and the result contains no radical. Pairs of radical terms like, are called conjugate pairs.

Rationalizing Denominators with Two Terms  The sum and difference of the same terms are called conjugate pairs.  To rationalize denominators with two terms, we multiply the numerator and denominator by the conjugate of the denominator.

Solution Rationalize the denominator: Example 1 1

Solution Rationalize the denominator: Example

Solution Rationalize the denominator: Example

Terms with Differing Indices To multiply or divide radical terms with different indices, we can convert to exponential notation, use the rules for exponents, and then convert back to radical notation.

Solution Multiply and, if possible, simplify: Converting to exponential notation Adding exponents Converting to radical notation Simplifying Example

Group Exercise Simplify the following radical expressions