Given a positive real number a, there are two solutions to the equation #x^2=a#, one is positive, and the other is negative. We denote the positive root (which we often call the square root) by #\sqrt{a}#. The negative solution of #x^2=a# is #−\sqrt{a}# (we know that if #x# satisfies #x^2=a#, then #(−x)^2=x^2=a#, therefore, because #\sqrt{a}# is a solution, so is #−\sqrt{a}#). So, for #a>0, \sqrt{a}>0#, but there are two solutions to the equation #x^2=a#, one positive #(\sqrt{a})# and one negative #(−\sqrt{a})#. For #a=0#, the two solutions coincide with #\sqrt{a}=0#.

As we all know a square root is occurrence when an integer n is multiplied to itself to give us an integer n* n. We also know when 2 integers with the same signs are multiplies it gives a positive integer .

with a these facts in mind we can say that n can be negative or positive and still give us the same perfect square.

PS . note that something like #sqrt{-1} # wouldn't exist as we know that 2 integers with opposite symbols will not give a negative number.And for it to be a square number both the nos . have to be same.

Hopefully this helps