Explanation:

The question presents a $3 \times 3$ grid of numbers. We need to find the missing number in the third row, third column. First, observe the first row: $25, 36, 49$. These are perfect squares: $5^2, 6^2, 7^2$. Let's denote the numbers in the grid as $C_{ij}$ where $i$ is the row and $j$ is the column. Let's consider the relationship between the square root of the first row number and the numbers in the second and third rows for each column. For Column 1: $\sqrt{C_{11}} = \sqrt{25} = 5$. We observe that $\sqrt{C_{11}} + C_{21} = 5 + 12 = 17$, which matches $C_{31}$. For Column 2: $\sqrt{C_{12}} = \sqrt{36} = 6$. We observe that $\sqrt{C_{12}} + C_{22} = 6 + 13 = 19$, which matches $C_{32}$. The pattern is: The number in the third row is the sum of the square root of the number in the first row and the number in the second row for the respective column. Applying this pattern to Column 3: $\sqrt{C_{13}} = \sqrt{49} = 7$. The missing number $C_{33}$ will be $\sqrt{C_{13}} + C_{23} = 7 + 15 = 22$. Let's analyze the options: A) $21$: Incorrect. B) $23$: Incorrect. C) $22$: This option perfectly matches the derived pattern. D) $24$: Incorrect.