No, the square of an integer cannot be negative. Let’s break this down to understand why.
An integer is a whole number that can be either positive, negative, or zero. When you square an integer, you multiply that number by itself. For example:
- If you take a positive integer, say 3, and square it (3 x 3), you get 9, which is positive.
- If you take a negative integer, for instance, -3, and square it (-3 x -3), you also get 9, which is again positive.
- Even if you square zero (0 x 0), the result is 0, which is neither positive nor negative.
This means that no matter what integer you start with—whether it’s positive, negative, or zero—the result of squaring it will always be a non-negative number (0 or positive).
In mathematical terms, for any integer x, the square is represented as x². The square x² is always greater than or equal to 0:
- x² ≥ 0 for all integers
Conclusively, it can be stated that the square of an integer cannot be negative, making this concept a fundamental property of integers in mathematics.