Rational Exponents and Nth Roots Objectives:

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Presentation transcript:

Rational Exponents and Nth Roots Objectives: Be able to determine the types of solutions a nth root will have. Be able to evaluate basic nth roots. Be able to evaluate a nth root with a calculator. Be able to solve equations using nth roots. Critical Vocabulary: nth root

I. Solutions of a nth root nth root of a Let “n” be an integer (n > 1) and let “a” be a real number n is an even integer n is an odd integer a < 0: No real nth roots a < 0: One real nth root a = 0: One real nth root a = 0: One real nth root a > 0: Two real nth roots a > 0: One real nth root

II. Evaluate a nth root nth root of a 2nd root of 4 3rd root of 27 4th root of 256 4th root of -16 No Solution 3rd root of -8

II. Evaluate a nth root (calculator) 2 3 4 No Solution -2

III. Evaluate Complex Roots

IV. Solving Equations Using nth Roots 1. 4x5 = 128 2. (x + 5)4 = 16 3. (x - 8)5 = 100 x5 = 32 x = 2

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