What smallest number should be added to the sum of squares of 15 and 14, so that the resulting number is a perfect square ?
A 17 B 20 C 11 D 9

Options

A. A
B. C
C. D
D. B

Answer

To solve the problem, we need to find the smallest number that should be added to the sum of the squares of 15 and 14 so that the result is a perfect square.

### Step-by-Step Solution:

1. **Calculate the squares of 15 and 14**:
- \( 15^2 = 225 \)
- \( 14^2 = 196 \)

2. **Find the sum of these squares**:
- \( 225 + 196 = 421 \)

3. **Identify the nearest perfect squares around 421**:
- The perfect square just below 421 is \( 20^2 = 400 \).
- The perfect square just above 421 is \( 21^2 = 441 \).

4. **Determine how much needs to be added to reach the next perfect square**:
- To find the smallest number to add to 421 to reach 441:
- \( 441 - 421 = 20 \)

5. **Conclusion**:
- The smallest number that should be added to the sum of squares of 15 and 14 to make it a perfect square is **20**.

### Final Answer:
**B. 20**