7.1 nth Roots and Rational Exponents

1. 7.1 nth Roots and Rational Exponents p. 401 What is a quick way to tell what kind of real roots you have? How do you write a radical in exponent form? What buttons do you use on a calculator to approximate a radical? What is the difference between evaluating and solving?

2. Real nth Roots Let n be an integer greater than 1 and a be a real number. If n is odd, then a has one real nth root. If n is even and a > 0, then a has two real nth roots. If n is even and a = 0, then a has one nth root. If n is even and a < o, then a has no real nth roots.

3. Find the indicated real nth root • n = 3, a = −125 • n = 4, a = 16

4. Rational Exponents Let a1/n be an nth root of a, and let m be a positive integer.

5. Evaluate the expression with Rational Exponents • 93/2 • 32-2/5

6. Using a calculator to approximate a root Rewrite the problem as 53/4 and enter using ^ or yx key for the exponent.

7. Solve the equation using nth roots. • 2x4 = 162 x4 = 81 x4 = 34 x = ±3 • (x − 2)3 = 10 x ≈ 4.15

8. Turn to Page 403 • Evaluating a model with roots. • Solving an equation using an nth root.

9. What is a quick way to tell what kind of real roots you have? Root is odd, 1 answer; root is even, 1 or 2 real answers. • How do you write a radical in exponent form? Use a fraction exponent (powers go up, roots go down) • What buttons do you use on a calculator to approximate a radical? Root buttons • What is the difference between evaluating and solving? Evaluating simplifies; Solving finds answers x=.

10. Assignment • Page 404, 13-61 odd To get credit for doing the problem, you must show the original problem along with your answer unless it is a calculator problem (41-51)