Evaluate cube root of 512

Problem

√(3,512)

Solution

1. Identify the goal, which is to find a number that, when multiplied by itself three times, equals 512

2. Prime factorize the number 512 to see its base components.

512=2⋅256

512=2⋅2⋅128

512=2⋅2⋅2⋅64

512=2⋅2⋅2⋅2⋅32

512=2⋅2⋅2⋅2⋅2⋅16

512=2⋅2⋅2⋅2⋅2⋅2⋅8

512=2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2

3. Group the factors into three identical sets to find the cube root.

512=(2⋅2⋅2)⋅(2⋅2⋅2)⋅(2⋅2⋅2)

512=8⋅8⋅8

512=8

4. Apply the cube root operation to the result.

√(3,8)=8

Final Answer

√(3,512)=8

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