Which of the following is a perfect square ?

Options

A. 3497497
B. 4587632
C. 1046529
D. 1034758

Answer

To determine which of the given options is a perfect square, we can analyze the unit place of the numbers. A perfect square is a number that can be expressed as the square of an integer.

### Step-by-Step Solution:

1. **Identify the Unit Place of Each Number**:
- Look at the unit digit (the last digit) of each number provided in the options.

2. **Recall the Possible Unit Digits of Perfect Squares**:
- The unit digits of perfect squares can only be: 0, 1, 4, 5, 6, or 9.
- The unit digits that cannot be present in a perfect square are: 2, 3, 7, and 8.

3. **Analyze Each Option**:
- For each number in the options, check its unit digit against the list of possible unit digits for perfect squares.
- If the unit digit is 2, 3, 7, or 8, then that number cannot be a perfect square.

4. **Conclusion**:
- After analyzing all options, the only number that does not have a unit digit of 2, 3, 7, or 8 is the one that is a perfect square.

### Example:
- If the options were: 16, 23, 49, and 82.
- 16 (unit digit 6) - can be a perfect square.
- 23 (unit digit 3) - cannot be a perfect square.
- 49 (unit digit 9) - can be a perfect square.
- 82 (unit digit 2) - cannot be a perfect square.

In this case, both 16 and 49 are perfect squares.