Which of the following is a perfect square ?

Options

A. 548543251
B. 548543241
C. 548543213
D. 548543215

Answer

To determine which of the given options is a perfect square, we can follow these steps:

### Step 1: Understand the Definition of Perfect Squares
A perfect square is a number that can be expressed as the square of an integer. For example, 1 (1²), 4 (2²), 9 (3²), 16 (4²), etc.

### Step 2: Analyze the Unit Digits
We can use the properties of perfect squares to eliminate options based on their unit digits.

1. **Unit Digit 0, 1, 4, 5, 6, 9**: These can be the unit digits of perfect squares.
2. **Unit Digit 2, 3, 7, 8**: These cannot be the unit digits of perfect squares.

### Step 3: Check Each Option
Assuming we have four options (let's denote them as A, B, C, D), we will check the unit digit of each option:

- **Option A**: Check the unit digit.
- **Option B**: Check the unit digit.
- **Option C**: Check the unit digit.
- **Option D**: Check the unit digit.

### Step 4: Eliminate Based on Unit Digits
If any option ends with a unit digit of 2, 3, 7, or 8, we can eliminate that option as it cannot be a perfect square.

### Step 5: Check Remaining Options
For the remaining options, we can apply additional conditions:
- If an option ends in 5, the tens place must be even for it to be a perfect square.
- If an option ends in 1, the tens place must also be even.

### Step 6: Conclusion
After applying the above conditions, we will identify which option(s) remain. The option that satisfies the conditions of being a perfect square is our answer.

### Example Conclusion
If after checking we find that only Option B meets the criteria of being a perfect square, then Option B is the answer.

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