Section 10.5

1. Section 10.5 Expressions Containing Several Radical Terms

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

3. Example Simplify by combining like radical terms. Solution

4. Example Simplify by combining like radical terms. Solution

5. Examples Simplify the following expressions

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

7. Solution Using the distributive law F O I L

8. 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.

9. 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.

10. Example Rationalize the denominator: Solution 1 1

11. Example Rationalize the denominator: Solution

12. Example Rationalize the denominator: Solution

13. 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.

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

15. Group Exercise Simplify the following radical expressions