The greatest 4 digit number which is a perfect square, is

Options

A. 9999
B. 9909
C. 9801
D. 9081

Answer

To find the greatest 4-digit number that is a perfect square, we can follow these steps:

### Step 1: Identify the greatest 4-digit number
The greatest 4-digit number is 9999.

### Step 2: Find the square root of the greatest 4-digit number
To determine if 9999 is a perfect square, we need to find its square root. We can approximate the square root of 9999.

\[ \sqrt{9999} \approx 99.995 \]

### Step 3: Determine the largest integer less than or equal to the square root
The largest integer less than or equal to 99.995 is 99. Therefore, we will check the square of 99.

### Step 4: Calculate the square of 99
Now, we calculate:

\[ 99^2 = 9801 \]

### Step 5: Verify that 9801 is a 4-digit number and a perfect square
9801 is indeed a 4-digit number, and since it is the square of 99, it is a perfect square.

### Conclusion
Thus, the greatest 4-digit number which is a perfect square is:

\[ \boxed{9801} \]

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