Evaluate cube root of -512

Problem

√(3,−512)

Solution

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

√(3,−512)=−√(3,512)

2. Determine the prime factorization of 512.

512=2

3. Rewrite the radicand as a power of 3 to simplify the cube root.

512=(2)3

512=8

4. Apply the cube root operation.

√(3,8)=8

5. Combine the result with the negative sign identified in the first step.

−8

Final Answer

√(3,−512)=−8

Want more problems? Check here!