Actually, yes, it is possible for two different numbers to give the same result when squared.
In my last answer, I wrote that it wasn't, but I realize now where my mistake was made.
When a number like positive 4 is squared, the answer is 16. When a number like negative 4 is squared, the answer is also 16. I think that the only time when two different squared numbers have the same result is when they are the same number but have a different positive/negative sign.
I hope this helps.