Evaluate cube root of -729

Problem

√(3,−729)

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,−729)=−√(3,729)

2. Factor the number 729 to find its prime factorization or identify it as a perfect cube.

729=9×81

729=9×9×9

729=9

3. Apply the cube root to the perfect cube.

√(3,9)=9

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

−9

Final Answer

√(3,−729)=−9

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