The greatest 3 digit number which is a perfect square is

Options

A. 729
B. 927
C. 961
D. 972

Explanation

To find the greatest 3-digit number that is a perfect square, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the range of 3-digit numbers**:
The smallest 3-digit number is 100 and the largest is 999.

2. **Find the square root of the largest 3-digit number (999)**:
We need to determine the largest integer whose square is still a 3-digit number.
\[ \sqrt{999} \approx 31.62 \]
This means the largest integer we can use is 31.

3. **Calculate the square of 31**:
Now, we will square 31 to check if it is a 3-digit number.
\[ 31 \times 31 = 961 \]

4. **Check the next integer (32)**:
To ensure that 961 is the greatest 3-digit perfect square, we will also check the square of 32.
\[ 32 \times 32 = 1024 \]
Since 1024 is a 4-digit number, we confirm that 961 is indeed the greatest 3-digit perfect square.

5. **Conclusion**:
Thus, the greatest 3-digit number which is a perfect square is **961**.