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Nth Root and Rational Exponents Section 7.1

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WHAT YOU WILL LEARN: 1.How to evaluate nth roots of real numbers using both radical notation and rational exponent notation. 2.How to use nth roots to solve real-life problems.

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Roots Other than Squares 2 3 is 8 We can also say the cube root of 8 is 2. (What number times itself 3 times is 8) This is more commonly written The number written outside of the radical sign is called the index and tells you what root you are looking for.

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Rational Exponents Roots can also be written as rational exponents. For example: can be rewritten as 16 ½ How do you think you would rewrite the following?

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Some Examples Find the indicated real n th root(s) of a. 1. n = 3, a = -125 2. n = 4, a = 16

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More About Rational Exponents Rational exponents do not have to have a numerator of 1. For instance: The denominator is the index or root of the number under the radical. The numerator is the power that you raise the “ answer ” to.

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“ Mathy ” Definition Let a 1/n be an nth root of a, and let m be a positive integer. a m/n = (a 1/n ) m = a -m/n =

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Some Examples Evaluate the following: 1. 2.

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You Try Evaluate the following: 1. 2.

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Using a Calculator Evaluate

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Solving Equations with Roots Solve the following: 1. 2x 4 = 162 2. (x – 2) 3 = 10

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You Try Solve the following: 1. 6x 4 = 3750 2. (x + 1) 3 = 18

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A Lovely Word Problem The volume for the volume V of a regular dodecahedron is v = 7.66a 3 where a is the length of an edge of the dodecahedron. Find the length of an edge of a regular dodecahedron that has a volume of 30 cubic feet.

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Homework Homework: page 404, 14-22 even, 30-44 even, 48, 54-60 even, 66

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