Evaluate cube root of -125/343

Problem

√(3,−125/343)

Solution

1. Apply the property of radicals for fractions, which states that the cube root of a quotient is the quotient of the cube roots.

√(3,−125/343)=√(3,−125)/√(3,343)

2. Extract the negative sign from the cube root, as the cube root of a negative number is negative.

√(3,−125)/√(3,343)=−√(3,125)/√(3,343)

3. Identify the perfect cubes for the numerator and denominator.

125=5

343=7

4. Evaluate the cube roots by taking the base of each perfect cube.

√(3,125)=5

√(3,343)=7

5. Combine the results into the final fraction.

−5/7

Final Answer

√(3,−125/343)=−5/7

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