1. Chapter 7.1 Roots & Radical Expressions

2. Definitions/Key Concepts 5 2 _______, 5 is a ________ root of 25 5 3 _______, 5 is a ________ root of 125 5 4 _______, 5 is a ________ root of 625 Definition of n th root for REAL NUMBERS: a n = b means a is the n th root of b 25square 125cube 625fourth

3. Summary of Possible Real Roots Type of Number # of REAL n th roots, when n is even # of REAL n th roots, when n is odd Positive21 011 Negative01 EXAMPLE: Find All Real Roots A)The cube root of 27 = _______ B)The fourth root of 81 = _______ C)The sixth root of -64 = ________ D)The cube root of -8/27 = _______ E)The fourth root of 16/81 = _______ F)The cube root of 0.008 = ________ 3 + 3 No real roots -2/3 + 2/3 0.2

4. Radical Signs! You can use a radical sign to indicate the root. The Index gives the degree of the root. The radicand is the number under the radical sign.

5. Steps To Finding Real Roots Step 1: Deal with the NUMBERS first (if any). Use calculator as necessary. Step 2: With Variables Inside the Radicand: You can just divide the exponent by the INDEX. The whole number comes out of the radical, and the remainder (if any) stays inside the radical. Step 2: Simplify the Expression Example: 9x 10 IMPORTANT NOTE: ONLY USE ABSOLUTE VALUE SYMBOLS WHEN THE INDEX IS EVEN AND THE SIMPLIFIED EXPRESSION CONTAINS A VARIABLE WITH AN ODD DEGREE

6. Additional Examples 3 a3b3a3b3 x 16 y 4 4 5 32x 20 y 17