Proving that sequences with the pattern aaaaaaa don't include a perfect square I need help with the following problem:

Which of the following sequences doesn't have perfect square:
A) $11, 111, 1111, \dots$
B) $33, 333, 3333, \dots$
C) $44, 444, 4444, \dots$
D) $77, 777, 7777, \dots$

I proved that the first sequence cannot contain a perfect square, but it seems that none of them contains a perfect square. Is it possible to  write a proof for a general pattern $aaaaaaaaa$?

No square ends in $3$ or in $7$.
No square ends in $11$.
But some squares end in $44$, but never mind if $44\cdots 44$ is a square,
so is $11\cdots11$ which isn't.
