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That number was obtained by finding the volume of the cube. This is done by multiplying the length of the figure by its width and then by its height. That is, by multiplying one number by another number and then by a third number. For a cube, the length, width, and height are all equal, or the same number. Finding the volume of a cube therefore involves multiplying a number by itself and then by itself again. This brings us to the general definition of the cube of a number. The cube of any number is that number multiplied by itself, and then the product multiplied by the original number. For example, 729 is the cube of 9 because you have to multiply 9 by itself (9) to get 81, and then multiply 81 by 9 to get 729. The number that gets multiplied to make the cube value is the root of that cube, or the 'cube root'.
This is the basis of the general definition of a cube root. The cube root of a number is whatever number must be multiplied by itself and then by that product ('cubed') in order to get the original number. For example, 3 is the cube root of 27 because 3 must be multiplied by 3 (itself) to get 9, and then 9 must be multiplied by 3 to get 27. These relationships are true for any number.