Question

Check whether the $400$ are perfect cubes?

Answer 1

Prime Factorisation Method to Find a Cube:

The perfect cube is the result of multiplying the same integer three times.

Let us check the numbers by prime factorizing.

$$\begin{gathered} 400=2\times 2\times 2\times 2\times 5\times 5 \\ 400=2^3\times 2^1\times 5^2 \end{gathered}$$

$\because 2$ and $5$ do not occur in a triplet.

Hence, $400$ is not a perfect cube.