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1 Algebra 2: Section 7.1 Nth Roots and Rational Exponents

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7.1: Evaluating nth Roots You are familiar with square roots –2 is the square root of 4, since 2 2 = 4. This concept can be extended to other types of roots –2 is the cube root of 8, since 2 3 = 8 –2 is the fourth root of 16, since 2 4 = 16 –2 is the fifth root of 32, since 2 5 = 32 –2 is the nth root of a, since 2 n = a

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3 Rational Exponents

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4 Examples Rewrite using rational exponents. Rewrite using radical notation.

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5 Nth Roots Rules for Signs of Answers For odd roots (3, 5, 7, etc) –There is ALWAYS ONLY ONE answer (either + or -) For even roots (2, 4, 6, etc) –If the radical symbol is already in the problem, then use the sign that is in front –If YOU put the radical symbol in the problem to solve an equation, then there will be two answers (+ and -)

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6 Examples Find the nth root(s) of a 7. n = 5, a = -32 8. n = 3: a = 64 9. n = 4: a = 256 10. n = 2: a = 169 What multiplied by itself 5 times equals -32? What multiplied by itself 3 times equals 64? What multiplied by itself 4 times equals 256? What multiplied by itself 2 times equals 169?

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Examples Simplify or evaluate each expression: 7

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Rational Exponents (examples) Simplify or evaluate each expression: 14.8 2/3 15.16 3/4 16.4 -5/2

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9 Examples Solve the equation. Round your answer to two decimal places.

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Examples 10

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11 Homework P.404 #13-22 all #24-40 evens #53-61 all

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List of Perfects Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 Perfect Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 Perfect Quads: 1, 16, 81, 256, 625 Perfect Fifths: 1, 32, 243, 1024, 3125

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