Evaluate cube root of 32

Problem

√(3,32)

Solution

1. Identify the number under the radical and look for its prime factorization.

32=2×2×2×2×2

2. Group the factors into sets of three, as the index of the radical is 3.

32=2×2

3. Apply the property of radicals where √(n,a×b)=√(n,a)×√(n,b)

√(3,32)=√(3,2×2)

4. Simplify the radical by taking the cube root of the perfect cube.

√(3,2)×√(3,2)=2×√(3,4)

Final Answer

√(3,32)=2√(3,4)

Want more problems? Check here!