The smallest non-palindromic number whose square is a palindrome?

Answer 1

That would be 26 . . . its square is 676.

There are two smaller palindromic squares . . . 121 and 484 ... but they're the squares of

11 and 22 respectively, which are palindromic, so they flunk the question's specifications.

Answer 2

1 is the palindrome with square 1.
every single digit number is a palindrome.

Answer 3

11