Question

The number representing both a square number and a triangular number is

• A. $16$
• B. $36$
• C. $9$
• D. $25$

Answer 1

The correct option is B

$36$

The explanation for the correct option

Option B :$36$

$$\begin{gathered} \mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.} \\ \mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.} \\ \mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.} \\ \mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.} \\ \mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.} \\ \mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{}\mathbf{.} \end{gathered}$$ AND $$\begin{gathered} \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{.} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.} \\ \mathbf{}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.} \\ \mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.} \\ \mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.}\mathbf{}\mathbf{.} \end{gathered}$$

The explanation for the incorrect option

Option A :$16$ , can be represented as a square, not as a triangle

Option C : $9$ , can be represented as a square, not as a triangle

Option D: $25$ , can be represented as a square, not as a triangle

Hence , Option B is the correct answer.