1. Warm-up Simplify each expression. 1. 2. 3. 4. 5.

2. Unit 7: Radical Functions and Rational Exponents Section 7-1: Roots and Radical Expressions Goal 1.01: Simplify and perform operations with rational exponents and logarithms (common and natural) to solve problems.

3. nth root For any real numbers a and b, and any positive integer n, if then a is an nth root of b. Type of NumberNumber of Real nth Roots When n is Even Number of Real nth Roots When n is Odd Positive21 011 NegativeNone1

4. Key Terms Radical Sign: Used to indicate a root Radicand: The number under the radical sign Index: The degree of the root Principal Root: When a number has two real roots, the positive root is the principal

5. Property For any negative real number a – when n is even Example:

6. Radical Expressions

7. Finding all Roots Find all cube roots

8. Find all fourth roots

9. Simplify Radicals with variables

10. Additional Examples

11. Classwork/ Homework Classwork: P. 366 #1-12 All Homework: P. 366 #14-32 Even