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Published byEleanor Tucker Modified over 4 years ago

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You should know or start to recognize these: 2 2 = 43 2 = 94 2 = 165 2 = 25 2 3 = 83 3 = 274 3 = 645 3 = 125 2 4 = 163 4 = 814 4 = 2565 4 = 625 2 5 = 323 5 = 2434 5 = 1024 5 5 = 3125

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Chapter 7 Section 1 Roots and Radical Expressions

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5 2 = 255 is a square root of 25 Since 5 2 = 255 is a square root of 25 5 3 = 1255 is a cube root of 125 Since 5 3 = 1255 is a cube root of 125 5 4 = 6255 is a fourth root of 625 Since 5 4 = 6255 is a fourth root of 625 5 5 = 31255 is a fifth root of 3125 Since 5 5 = 31255 is a fifth root of 3125

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**Roots and Exponents are inverse operations** For any real numbers a and b, and any positive integer n, if a n = b then a is the n th root of b. Note: We are now working in REAL numbers only. (This means we will not be using i for any of our answers)

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If the root is even then there can be two answers is the principal root which indicates a positive answer is the other root which indicates a negative answer index radicand radical sign If the root is odd then there can be only one answer (the same sign as the radicand)

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Find each real-numbered root

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Simplify these Radical Expressions

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Simplifying Radical Expressions Hint: –Divide the exponent by the index, write how many times it goes in evenly and what is left over Absolute Value symbols are needed when you have an even root that results in an odd exponent (see previous examples)

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