Evaluate cube root of -8/27

Problem

√(3,−8/27)

Solution

1. Apply the property of radicals for fractions, which allows the cube root to be distributed to both the numerator and the denominator.

√(3,−8/27)=√(3,−8)/√(3,27)

2. Evaluate the cube root of the numerator. Since (−2)×(−2)×(−2)=−8 the cube root of −8 is −2

√(3,−8)=−2

3. Evaluate the cube root of the denominator. Since 3×3×3=27 the cube root of 27 is 3

√(3,27)=3

4. Combine the results to find the final simplified fraction.

(−2)/3=−2/3

Final Answer

√(3,−8/27)=−2/3

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