1. Choose a number with repeating 3's and a final 8.
2. The square is made up of:
   • the same number of 1's as there are repeating 3's in the number;
   • one 4
   • one fewer 2 than there are repeating 3's;
   • a final 44.

   Example:

1. If the number to be squared is 33338:
2. The square has:

   four 1's (same as
   repeating 3's)     1 1 1 1
one 4                         4
three 2's (one fewer than
   repeating 3's)               2 2 2
a final 44                            4 4

3. So the square of 33338 is 1,111,422,244.

   See the pattern?

1. If the number to be squared is 3333338:
2. The square has:

   six 1's (same as
   repeating 3's)   1 1 1 1 1 1
one 4                           4
five 2's (one fewer than
   repeating 3's)                 2 2 2 2 2
a final 44                                  4 4

3. So 3333338 × 3333338 = 11,111,142,222,244.