7.1 Warm-Up Evaluate the expression: √ √ √ Solve each equation. 2. – 121 √ 1. 9 3. ( 25 ) 2 √ 3 - 11 25 Solve each equation. 4. x² = 49 x = -7, 7

7.1 Roots and Radical Expressions Objective: To learn how to evaluate nth roots of real numbers using both radical notation and rational exponent notation. State Standard: 15.0 Students determine whether a specific algebraic statement involving radical expressions is sometimes true, always true, or never true. ================================================

7.1 Roots and Radical Expressions ⁿ √ a nth root of a: index: the integer n (greater than 1) is an nth root of a. 2³ = 8 2 is a cube root of 8 34 = 81 3 is a fourth root of 81

-2 4 Example 1: Find the indicated real nth root(s) of a. A. n = 5, a = -32 Radical Notation Exponential Notation 5 -32 √ B. n = 3, a = 64 (-32) 1/5 64 3 √ 1/ 3 64 -2 4

-3 3 On White Board Find the indicated real nth root(s) of a. -27 √ 1. n = 3, a = -27 3 -27 √ 2. n = 4, a = 81 (-27) 1/3 81 4 √ 1/ 4 81 -3 3

2xy2 -3c2 x2y3 On White Board Simplify 4x2y4 √ 22x2(y2)2 √ -27c6 √ 1. 2. 22x2(y2)2 √ -27c6 3 √ (-3)3(c2)3 3 √ 3. x8y12 4 √ 2xy2 (x2)4(y3)4 4 √ -3c2 x2y3

Let a be an nth root of a, and let m be a positive integer. RATIONAL EXPONENTS Let a be an nth root of a, and let m be a positive integer. 1/n a = (a ) = ( a ) m/n 1/n m n √ a = 1 = 1 , a = 0 a (a ) -m/n m/n 1/n m Example 2 a. 16 = ( 16) = 4 = 5/2 5 √ 1024 16 = (16 ) = 4 = 5/2 1/2 5 1024

7.1 Guided Practice Page 378 5, 9, 13 – 23 odd

7.1 HOMEWORK Page 378 5, 9, 13 – 23 odd, 26 – 28, 43 – 49