Evaluate fifth root of -1024

Problem

√(5,−1024)

Solution

1. Identify the index and the radicand of the expression. The index is 5 (an odd number) and the radicand is −1024

2. Determine the sign of the result. Since the index is odd and the radicand is negative, the result will be a negative number.

3. Find the prime factorization of the absolute value of the radicand.

1024=2

4. Rewrite the power to match the index of the root.

1024=(2)5

1024=4

5. Apply the property of odd roots √(n,−a)=−√(n,a)

√(5,−1024)=−√(5,1024)

6. Simplify the radical expression.

−√(5,4)=−4

Final Answer

√(5,−1024)=−4

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