Evaluate cube root of -216

Problem

√(3,−216)

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 radicand as a power. We look for a number that, when multiplied by itself three times, equals 216

3. Determine the base of the power. Since 6×6×6=216 it follows that (−6)×(−6)×(−6)=−216

4. Simplify the expression by applying the rule √(3,a3)=a

Final Answer

√(3,−216)=−6

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