Evaluate cube root of -1000

Problem

√(3,−1000)

Solution

1. Identify the base and the index of the radical expression. The base is −1000 and the index is 3

2. Rewrite the base as a power of a number. Since the index is odd, we look for a number that, when multiplied by itself three times, equals −1000

3. Determine the value. We know that 10×10×10=1000 so (−10)×(−10)×(−10)=−1000

4. Simplify the expression by applying the property √(n,an)=a for odd n

Final Answer

√(3,−1000)=−10

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