A cube root, as well as a perfect cube, are both numbers and, as numbers, they have no dimensions.
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A cube root of a perfect cube has only one dimension. A perfect cube is a number that can be obtained by multiplying an integer by itself three times. Taking the cube root of a perfect cube will give you the original integer value, effectively reducing the dimensionality back to one.
an integer
It can take on many dimensions but if its a cube then the cube root of 800 will give its equal dimensions in mm
4096
a perfect cube
The square root of a perfect square and the cube root of a perfect cube is always an integer. A perfect square is a number multiplied by itself. A perfect cube is a number multiplied by itself twice. Example: 3 x 3 is 9, the square of 3 3 x 3 x 3 is 27, the cube of 3