Algebra 2 Bellwork – 3/4/15

6.1 Evaluate nth Roots and Use Rational Exponents

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

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

Radicals If n is odd – one real root. If n is even and a > 0 Two real roots a = 0 One real root a < 0 No real roots

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

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

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

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

Example 3: Evaluate Without a Calculator

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.

Ex. 5 Evaluating Expressions with Rational Exponents B. Using radical notation Using rational exponent notation. OR OR

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

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

Homework due 3/4/15 Page 417: 3-18 All