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Roots of Real Numbers and Radical Expressions

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Definition of n th Root ** For a square root the value of n is 2. For any real numbers a and b and any positive integers n, if a n = b, then a is the nth root of b.

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Notation index radical radicand Note: An index of 2 is understood but not written in a square root sign.

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Simplify To simplify means to find x in the equation: x 4 = 81 Solution: = 3

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Principal Root The nonnegative root of a number Principal square root Opposite of principal square root Both square roots

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Summary of Roots even odd one (+) root one (-) root one (+) root no (-) roots no real roots no (+) roots one (-) root one real root, 0

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Examples

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When to use absolute value signs If the index (n) of the radical is even, the power under the radical sign is even, and the resulting power is odd, then we must use an absolute value sign. Even – Even – Odd …. ABSOLUTE VALUE SIGNS!

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Examples Even Odd

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Even Odd Even 2

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Classwork: 1) 5) 2) 6) 3) 7) 4) 8)

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+ 7.2 The Real nth Roots of a Number. + 1. How many values in the domain of f are paired with the value in the range? That is, how many x values satisfy.

+ 7.2 The Real nth Roots of a Number. + 1. How many values in the domain of f are paired with the value in the range? That is, how many x values satisfy.

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