Study Guide for Chapter 9 & 10

Study Guide for Chapter 9 & 10 - MATH A Chapter 9...

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MATH A: Chapter 9 Study Guide, Roots and Radicals 9.1, Finding Roots Objectives: 1) Find Square Roots 2) Find higher roots. I. Fundamentals A. Square Roots 1. To find a square of a number – multiply by itself 2 a a a = 2. To find a cube of a number – multiply the number by itself 3 times. 3 a a a a = 3. To find a square root of a number – use the inverse process of squaring 4. To find a cube root of a number – use the inverse process of cubing. B. Radicals 1. n a b = 2. Definition of the Principal nth Root of a real number : If a is a nonnegative real number, and b is the nonnegative root of a, we can write n b a = , denoted by n a b = ,is the Principal nth Root of a. C. Finding perfect roots: Evaluate 1) 36 2) 9 - 3) 1 25 4) 36 64 + 5) 36 64 + D. See the table on page 552 for the perfect squares. II. Roots greater than square roots A. Definition of the principal nth root of a real number: n a b = means that n b a = . The natural number n is called the index. The index, 2, for square roots is usually omitted. B. Reversing nth Powers with nth Powers Roots Vocabulary Cube Roots 3 4 3 64 Index is ( 29 3 2 - 3 8 - 3 5 3 125 Fourth Roots 4 1 4 1 Index is 4 3 4 81 Fifth Roots 5 2 5 32 Index is Nth Roots n b n a Index is 1
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C. Finding Roots 1) 6 64 2) 3 1 125 3) 3 125 - 4. 4 - 5) 4 81 - 6) 3 3 8 - 7) 6 49 2 81 - 9.2, Multiplying and Dividing Radicals Objectives: 1) Multiply square roots. 2) Simplify square roots. 3) Use the quotient rule for square roots. 4) Use the product rule and quotient rule for other roots.
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