Simplify cube root of 32

Problem

√(3,32)

Solution

1. Find the prime factorization of the number inside the radical to identify perfect cubes.

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 product property of radicals to separate the perfect cube from the remaining factors.

√(3,32)=√(3,2⋅2)

√(3,32)=√(3,2)⋅√(3,2)

4. Simplify the radical by taking the cube root of the perfect cube and calculating the remaining power.

√(3,2)=2

√(3,2)=√(3,4)

Final Answer

√(3,32)=2√(3,4)

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