Evaluate cube root of 1/27

Problem

√(3,1/27)

Solution

1. Apply the quotient property of radicals, which states that the cube root of a fraction is the cube root of the numerator divided by the cube root of the denominator.

√(3,1/27)=√(3,1)/√(3,27)

2. Evaluate the numerator by finding the number that, when multiplied by itself three times, equals 1

√(3,1)=1

3. Evaluate the denominator by identifying that 27 is a perfect cube, specifically 3×3×3=3

√(3,27)=3

4. Simplify the fraction by substituting the calculated values back into the expression.

1/3

Final Answer

√(3,1/27)=1/3

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