Question

Is $$256$$ a perfect cube? In case of perfect cube, find the number whose cube it is.

Answer 1

A perfect cube can be expressed as a product of three same numbers

Now by resolving the given number into prime factors we get,

$$256\ =\ 2\ \times\ 2\ \times\ 2\ \times\ 2\ \times\ 2\ \times\ 2\ \times\ 2\ \times\ 2$$

Since the given number has more than three factors and we cannot make three pairs of same number.

$$\therefore$$ $$256$$ is not a perfect cube.