No, the square of an integer cannot be a negative number.
To understand why, let’s consider the definition of squaring a number. When you square an integer, you are multiplying that integer by itself. For example, if we take the integer 3 and square it, we get:
3 × 3 = 9
Similarly, if we take -3 and square it, we have:
-3 × -3 = 9
As you can see from these examples, regardless of whether the integer is positive or negative, the result of squaring it is always non-negative (zero or positive). This occurs because multiplying two negative numbers results in a positive number, and multiplying two positive numbers also results in a positive number.
In mathematical terms, the square of any integer ‘n’ can be expressed as:
n² = n × n
Since both ‘n’ and ‘n’ will either be positive or negative, the product will always be non-negative. Therefore, the square of any integer is always zero or a positive integer, confirming that a squared integer can never be negative.