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Algebra 2 Bellwork – 3/4/15

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**6.1 Evaluate nth Roots and Use Rational Exponents**

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

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**The nth Root Radical Index Number**

Radicand The index number becomes the denominator of the exponent.

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**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

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**Radical form to Exponential Form**

Change to exponential form. or or

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**Exponential to Radical Form**

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

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**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

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**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

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**Example 3: Evaluate Without a Calculator**

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**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.

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**Ex. 5 Evaluating Expressions with Rational Exponents**

B. Using radical notation Using rational exponent notation. OR OR

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**Example 6: Solving an equation**

Solve the equation: Note: index number is even, therefore, two answers.

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**Ex. 7 & 8 Solving Equations Using nth Roots**

A. 2x4 = 162 B. (x – 2)3 = 10

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Homework due 3/4/15 Page 417: All

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