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SECTION 6.1 I. Definition of an nth Root OBJECTIVES At the conclusion of this lesson you should be able to: 1. 2. II. Simplify radical expressions. Evaluate square roots. PROCEDURE While watching the video, follow this study guide and take notes in the study guide as if you were sitting in a classroom. Stop or pause the video as needed to catch up or copy something down. n a a Square root of a 3 a read as ____________________________________ 4 a read as ____________________________________ 5 a read as ____________________________________ n a read as ____________________________________ 195 Perfect Squares 12 = 1 6 2 = _____ 112 = _____ 16 2 = _____ 22 = 4 7 2 = _____ 12 2 = _____ 17 2 = _____ 3 2 = _____ 8 2 = _____ 13 2 = _____ 18 2 = _____ 4 2 = _____ 9 2 = _____ 14 2 = _____ 19 2 = _____ 5 2 = _____ 10 2 = _____ 15 2 = _____ 20 2 = _____ Perfect Cubes 13 = 1 6 3 = ______ 23 = 8 7 3 = ______ 33 = ______ 8 3 = ______ 4 3 = ______ 9 3 = ______ 5 3 = ______ 10 3 = ______ Perfect 4th’s 14 = 1 2 4 = 16 3 4 = ______ 4 4 = ______ 5 4 = ______ Perfect 5th’s 15 = 1 2 5 = 32 35 = ______ 4 5 = ______ 196 16 = − 49 = 3 256 = − 27 = even negative = NOT A REAL NUMBER odd negative = negative − 81 = 25 = 49 3 8= 3 −8 = 4 197 − 16 = Evaluating n a Page 499 1. If n > 1 is an even integer and a > 0 , then 2. If n > 1 is an odd integer, then 3. If n > 1 is an integer, n n a 1. an is the principal positive nth root of a. 0 =0 . Example for #2 16 = _____ n a is the nth root of a. Example for #1 Evaluating n 3 27 = _____ 3 − 27 = _____ Page 500 _________________________________________________________ n ______________________________________________ 2. an = a . _________________________________________________________ n ______________________________________________ an = a . Example for #1 Example for #2 3 23 = _______ 4 2 4 = _______ 3 (− 2)3 4 (− 2)4 = _______ 198 = _______ Turn in your textbook to page 505. Problem #52. (− 5)2 Problem #56. 5 = _____ Problem #54. 6 (50)6 6 = _______ a 8b 4 c12 64x8 49a 6b8c10 3 = _______ Problem #58. x2 y4 4 (− 2)5 − 27 a 6b 9 199 (− 417)6 = _______ 32 x10 5 − 4 16 x8 y16 a 4b 2 c6 (x − 3)2 6 64a12 200