



 
Hello, Very loosely (not a rigorous proof) if a number is a square, say n = zz and a prime p divides it, what do you think about p dividing z? If p didn't divide z but divides n this would imply 'part' of p divided one of the z's and the 'rest' of p divided the other.
However p is pime and can't be broken into parts thus p divides both z's and p^{2 } divides n. ^{†}(editor's note) This is often called the "Fundamental Theorem of Arithmetic".  


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