729
I am pretty sure you can figure this out on your own. Raise different numbers to the square, until you get a 4-digit result. Similary, calculate the cube of different numbers, until you get a 4-digit number. If you want the SAME number to be both a perfect square and a perfect cube, then it must be a power of 6. In that case, just experiment raising different numbers to the sixth power, until you get a 4-digit number.
729
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.
8 cubed = 512
-1
729
729
729, cube of 9 and square of 27
I believe there are 2 positive three-digit perfect cube numbers, that are even.
729
46*46*46 = 97336
I am pretty sure you can figure this out on your own. Raise different numbers to the square, until you get a 4-digit result. Similary, calculate the cube of different numbers, until you get a 4-digit number. If you want the SAME number to be both a perfect square and a perfect cube, then it must be a power of 6. In that case, just experiment raising different numbers to the sixth power, until you get a 4-digit number.
It could be any one of them: 3: A 1-digit perfect square - 1 which is not a perfect cube. 7: A perfect cube - 1 8: A 1-digit perfect square - 1 which is also a perfect cube. 15: A perfect 4th power - 1 30: More than 1 away from a perfect power.
729
4,096 = (64)2 = (16)3
For a number to be a perfect square and a perfect cube, it must be a perfect sixth power. Now 36 = 729 is too small and 56 = 15625 is too large, leaving 46 = 4096 as the answer.