Because for a number to be a square number it must have a number which when multiplied by it self=that number.
For example:
36 is a square number because 6x6=36
16 is a square number because 4x4=16
A negative number such as -16 is not a Square Number because -4x-4=16 not -16 because a negative times a negative is a positive. -4x4=-16 but these numbers aren't the same therefore -16 isn't a square number.
This is why negative numbers cant be Square Numbers
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There is no square root for a negative number. It is an imaginary number.
The square root of negative 168 is: ~12.9315 i
The square root of a negative number is known as an imaginary number. In this case, the square root of negative 37 would be represented as √(-37) = √37i, where "i" is the imaginary unit equal to the square root of -1. This means that the square root of negative 37 is the square root of 37 multiplied by the imaginary unit "i".
Square roots of negative numbers are what are called imaginary numbers. The building block of imaginary numbers is the symbol i which is defined as the square root of negative 1. The square root of other negative numbers can be expressed using i. For example, the square root of negative sixteen is 4i, the square root of negative nine is 3i and so on.