Perfect Cube

Perfect Cube

A number that is the cube of a whole number.

Examples

125 is a perfect cube, since 53 = 125 and 5 is a whole number.

25 is not a perfect cube, since $$\sqrt[3]{25}$$ is not a whole number.

Educational Note

The expression “perfect cube” should not be applied to just any algebraic expression.

The polynomial $${x}^{3}-6{x}^{2}+12x-8$$ which is equal to $${(x-2)}^{3}$$ can only be called a perfect cube if (x – 2) is a whole number. Instead, the polynomial $${x}^{3}-6{x}^{2}+12x-8$$ should be called the cube of the binomial (x – 2).