Question

Is the following number a perfect cube?
$46656$
Say yes or no.

• A. Yes
• B. No
• C. Ambiguous
• D. Data insufficient
  

Answer 1

The correct option is A Yes

On prime factorising, we get,

$46656=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 3\times 3$

$=2^6\times 3^6$.

We know, a perfect cube has multiples of $3$ as powers of prime factors.

Here, number of $2$'s is $6$ and number of $3$'s is $6$, which are multiples of $3$.

Hence, it is a perfect cube.

Therefore, option $A$ is correct.