The cube root of 1 will also be 1. You can check with the complementary operation: 1*1*1=1 (true).
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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.
The volume of a cube is determined by cubing the length of one edge, so the cube root of the volume will give you the length of an edge. (In a cube, all of the edges are the same length)
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2 cube root 6
What is the cube root of 17