1. 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

2. 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

3. 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

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

5. III. Evaluate Complex Roots

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

7. Page #3-45 odds, all
(31 problems)