1. Algebra 2 Bellwork – 3/4/15

2. 6.1 Evaluate nth Roots and Use Rational Exponents

3. Learning Target:
Evaluate nth roots of real numbers using both radical notation and rational exponent notation.

4. The nth Root Radical Index Number
Radicand
The index number becomes the denominator of the exponent.

5. Radicals If n is odd – one real root. If n is even and
a > Two real roots
a = One real root
a < No real roots

6. Radical form to Exponential Form
Change to exponential form. or or

7. Exponential to Radical Form
Change to radical form.
The denominator of the exponent becomes the index number of the radical.

8. Ex. 1 Finding nth Roots or Find the indicated real nth root(s) of a.
A. n = 3, a = -125
Solution: Because n = 3 is odd, a = -125 has one real cube root. Because (-5)3 =
-125, you can write: or

9. Ex. 2 Finding nth Roots or Find the indicated real nth root(s) of a.
A. n = 6, a = 729
Solution: Because n = 6 is even, a = 729 has two real sixth roots. Because 36 = 729,
you can write: or

10. Example 3: Evaluate Without a Calculator

11. Ex. 4 Approximating a Root with a Calculator
Use a scientific calculator to approximate:
SOLUTION: First rewrite as Then enter the following:
To solve simple equations involving xn, isolate the power and then take the nth root of each side.

12. Ex. 5 Evaluating Expressions with Rational ExponentsB.
Using radical notation
Using rational exponent notation. OR OR

13. Example 6: Solving an equation
Solve the equation:
Note: index number is even, therefore, two answers.

14. Ex. 7 & 8 Solving Equations Using nth Roots
A. 2x4 = 162
B. (x – 2)3 = 10

15. Homework due 3/4/15
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