Evaluate cube root of -1/8

Problem

√(3,−1/8)

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,−x)=−√(3,x)

2. Apply the property of radicals over a fraction, which allows the cube root to be distributed to both the numerator and the denominator.

√(3,−1/8)=−√(3,1)/√(3,8)

3. Evaluate the cube root of the numerator. The number that multiplied by itself three times equals 1 is 1

√(3,1)=1

4. Evaluate the cube root of the denominator. The number that multiplied by itself three times equals 8 is 2

√(3,8)=2

5. Combine the results into the final fraction.

−1/2

Final Answer

√(3,−1/8)=−1/2

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