Evaluate fifth root of -1

Problem

√(5,−1)

Solution

1. Identify the expression as the principal real fifth root of a negative number.

2. Recall that for any odd index n the nth root of a negative number is defined in the real number system and is negative.

3. Determine the value by finding a number which, when raised to the fifth power, equals −1

4. Calculate the result using the property (−1)5=−1

Final Answer

√(5,−1)=−1

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