Roots of Real Numbers and Radical Expressions

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Roots of Real Numbers and Radical Expressions
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Definition of nth Root
For any real numbers a and b and any positive
integers n, if an b, then a is the nth root
of b.
For a square root the value of n is 2.
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Notation
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 x4
81
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Principal Root
The nonnegative root of a number
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Summary of Roots
no real roots
one root one - root
even
one real root, 0
one root no - roots
no roots one - root
odd
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Examples
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Examples
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Taking nth roots of variable expressions Using
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.
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Examples
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