Determine the largest 4 digit number which is a perfect square.

Options

A. 9999
B. 9702
C. 9604
D. 9801

Answer

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

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

### Step 2: Find the square root of 9999.
To find the largest perfect square less than or equal to 9999, we need to calculate 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.

### Step 4: Calculate the perfect square of this integer.
Now, we calculate the square of 99:

\[ 99^2 = 9801 \]

### 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 largest 4-digit number which is a perfect square is **9801**.

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