Roots & Radical Expressions NOTES 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 Type of Number # of REAL nth roots, when n is even when n is odd Positive 2 1 Negative 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.

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

Important Property  

Additional Examples