Chapter 7.1 Roots & Radical Expressions

Chapter 7.1 Roots & Radical Expressions

Definitions/Key Concepts • 52 _______, 5 is a ________ root of 25 • 53 _______, 5 is a ________ root of 125 • 54 _______, 5 is a ________ root of 625 • Definition of nth root for REAL NUMBERS: an = b means a is the nth root of b 25 square 125 cube 625 fourth

Summary of Possible Real Roots • EXAMPLE: Find All Real Roots • The cube root of 27 = _______ • The fourth root of 81 = _______ • The sixth root of -64 = ________ 3 • The cube root of -8/27 = _______ • The fourth root of 16/81 = _______ • The cube root of 0.008 = ________ -2/3 + 3 + 2/3 No real roots 0.2

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.

9x10 Example: 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 IMPORTANT NOTE: ONLY USE ABSOLUTE VALUE SYMBOLS WHEN THE INDEX IS EVEN AND THE SIMPLIFIED EXPRESSION CONTAINS A VARIABLE WITH AN ODD DEGREE

5 32x20y17 3 a3b3 Additional Examples 4 x16 y 4

Chapter 7.1 Roots & Radical Expressions