Question

State whether true or false:
Is $1000$ a perfect cube?

• A. True
• B. False

Answer 1

The correct option is A True

Resolving $1000$ into prime factors, we find that

$1000=2\times 2\times 2\times 5\times 5\times 5$.

Clearly, the prime factors of $1000$ can be grouped into triples of equal factors and no factor is left over.

That is, $1000=2\times 2\times 2\times 5\times 5\times 5=2^3\times 5^3$.

$\therefore 1000$ is a perfect cube.

Hence, the given statement is true and option $A$ is correct.