What is the largest four digit number which is a perfect square?

Options

A. 9704
B. 9801
C. 9901
D. 9999

Answer

To find the largest four-digit number that is a perfect square, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the range of four-digit numbers**:
The smallest four-digit number is 1000, and the largest four-digit number is 9999.

2. **Determine the largest integer whose square is a four-digit number**:
We need to find the largest integer \( n \) such that \( n^2 \) is still a four-digit number. Since \( 10000 \) is a five-digit number, we will check \( n = 99 \) because \( 100^2 = 10000 \).

3. **Calculate the square of 99**:
\[ 99^2 = 99 \times 99 \]
To calculate \( 99^2 \):
- First, multiply \( 9 \times 9 = 81 \) (write down 1 and carry over 8).
- Then, calculate \( 9 \times 9 = 81 \) and add the carry over \( 8 \) from the previous step: \( 81 + 8 = 89 \).
- Finally, multiply \( 9 \times 9 = 81 \) again and add the carry over \( 8 \): \( 81 + 8 = 89 \).
- Therefore, \( 99^2 = 9801 \).

4. **Verify if 9801 is a four-digit perfect square**:
Since \( 9801 \) is a four-digit number and it is the square of \( 99 \), it is indeed a perfect square.

5. **Conclusion**:
The largest four-digit number which is a perfect square is \( 9801 \).

### Final Answer:
The largest four-digit number which is a perfect square is **9801**.