Evaluate fifth root of -243

Problem

√(5,−243)

Solution

1. Identify the index and the radicand of the expression. The index is 5 (an odd number) and the radicand is −243

2. Determine the sign of the result. Since the index is odd, the fifth root of a negative number is negative.

3. Find a number that, when multiplied by itself five times, equals 243 We test small integers: 3×3×3×3×3=243

4. Apply the negative sign to the result because (−3)5=−243

Final Answer

√(5,−243)=−3

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