The number 257 is not a perfect square because it ends in 7.
Perfect Squares and Last Digits
Certain digits can be immediately ruled out as possible last digits of perfect squares. As noted in the references, the last digit of a number can help determine if it cannot be a perfect square.
Reference Information
The provided references indicate the following regarding last digits and perfect squares:
- (ii) 257 ending with 7, so it cannot be a perfect square.
This information directly answers the question. Numbers ending in 2, 3, 7, or 8 cannot be perfect squares.
Explanation
A perfect square is an integer that can be expressed as the square of another integer. When we square integers, the last digit of the result follows a pattern. No integer squared will result in a number ending in 2, 3, 7, or 8. Therefore, if a number ends in one of these digits, it cannot be a perfect square.
Table of Possible Last Digits of Perfect Squares
| Last Digit of Original Number | Last Digit of Square |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 6 |
| 5 | 5 |
| 6 | 6 |
| 7 | 9 |
| 8 | 4 |
| 9 | 1 |
This table clearly shows that perfect squares can only end in 0, 1, 4, 5, 6, or 9.
