You can put this solution on YOUR website! Prove that no number of the type 4k+2 can be a perfect square.
If p is a prime factor of a perfect square, p^2 must also
be a factor of that perfect square.
4k+2 = 2(2k+1)
2 is a factor of 4k+2 but 2k+1 is odd and cannot have factor 2, so 4k+2 is not divisible by 4, and therefore cannot be a perfect square.