Evaluate cube root of 2/3

Problem

√(3,2/3)

Solution

1. Apply the quotient rule for radicals to separate the numerator and the denominator.

√(3,2/3)=√(3,2)/√(3,3)

2. Rationalize the denominator by multiplying both the numerator and the denominator by a factor that makes the radicand in the denominator a perfect cube.

√(3,2)/√(3,3)⋅√(3,3)/√(3,3)

3. Simplify the radicands by performing the multiplication inside the radicals.

√(3,2⋅9)/√(3,3⋅9)

4. Evaluate the denominator by taking the cube root of 27.

√(3,18)/√(3,27)

5. Write the final expression in its simplest radical form.

√(3,18)/3

Final Answer

√(3,2/3)=√(3,18)/3

Want more problems? Check here!