Evaluate cube root of 128

Problem

√(3,128)

Solution

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

2. Factor the number 128 into its prime components.

128=2⋅64

128=2⋅2⋅32

128=2⋅2⋅2⋅2⋅2⋅2⋅2

128=2

3. Group the factors into sets of three to simplify the cube root.

128=2⋅2⋅2

4. Apply the property of radicals √(3,a⋅b)=√(3,a)⋅√(3,b) to extract terms from the cube root.

√(3,2⋅2⋅2)

√(3,2)⋅√(3,2)⋅√(3,2)

5. Simplify the perfect cubes.

2⋅2⋅√(3,2)

4√(3,2)

Final Answer

√(3,128)=4√(3,2)

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