Evaluate cube root of -343

Problem

√(3,−343)

Solution

1. Identify the properties of cube roots. Since the index is odd, the cube root of a negative number is a negative number.

2. Rewrite the expression by pulling the negative sign out of the radical.

√(3,−343)=−√(3,343)

3. Determine the prime factorization or find a number that, when multiplied by itself three times, equals 343

7×7×7=49×7=343

4. Simplify the radical using the identified cube root.

−√(3,7)=−7

Final Answer

√(3,−343)=−7

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