Question

Which of the following numbers is a perfect cube?

• A. $243$
• B. $216$
• C. $392$
• D. $8640$

Answer 1

The correct option is B

$216$

Step 1. Explanation for the correct option.

As,

$$\begin{gathered} 216=6\times 6\times 6 \\ =6^3 \end{gathered}$$

So, it is a perfect cube as it be expressed as the product of triplets of prime factors.

Step 2. Explanation for the incorrect options.

$$\begin{gathered} 243=3\times 3\times 3\times 3\times 3 \\ =3^5 \\ 392=2\times 2\times 2\times 7\times 7 \\ =2^3\times 7^2 \\ 8640=2^6\times 3^3\times 5 \end{gathered}$$

So, these numbers are not a perfect cube as they cannot be expressed as the product of triplets of prime factors.

Hence, the correct option is $\mathrm{B}$.