What number is both a square number and a cube number?

Answer 1

The numbers 0 and 1 are self-squares and self-cubes, all exponentials being 0 and 1 respectively. Only a few other numbers are both squares and cubes of integers.

For any given square and cube, the numerical relation is n3 = [n(sqrt n)]2

so for the value n where (sqrt n) is whole number, the cube of n is also a square.

After 0 and 1, the next 4 are 64, 729, 4096, and 15625.

64 = 43 = 82 . (4x2)2

729 = 93 = 272 . (9x3)2

4096 = 163= 642 . (16x4)2

15625 = 253 = 1252 . (25x5)2

You can find the others easily. There are each the sixth power of any integer,

such that x6 = (x2)3 = (x3)2 e.g. 26 = 64, 36 = 729, 46 = 4096, etc. - Besides 64, another easy one is the number one million, 106, which is 1003 and 10002.

We can say that these numbers are the cube of a square, or the square of a cube, for any given integer.

Answer 2

The number that is both a square number and a cube number is 64. This is because 64 is equal to 8 squared (8 x 8 = 64) and also equal to 4 cubed (4 x 4 x 4 = 64). In mathematical terms, 64 is both a perfect square and a perfect cube.

Answer 3

Oh, what a happy little question! The number you're thinking of is 64. It's a square number because 8 x 8 equals 64, and it's also a cube number because 4 x 4 x 4 equals 64. Isn't it just wonderful how numbers can be both square and cube at the same time?

Answer 4

Well, darling, the number you're looking for is 1. It's a square because 1 multiplied by 1 gives you 1, and it's a cube because 1 multiplied by 1 multiplied by 1 also gives you 1. So, there you have it, 1 is both a square and a cube number.

Answer 5

4 8 64 100