1. Choose a number with repeating 6's and a final 2.
2. The square is made up of:
   • one fewer 4 than there are repeating 6's
   • 38
   • same number of 2's as 4's in the square
   • a final 44

   Example:

1. If the number to be squared is 6662:
2. The square has:

   two 4's (one fewer than
      repeating 6's)           4 4
Next digits: 38                    3 8
two 2's (same number as repeating 6's) 2 2
A final 44                                 4 4

3. So the square of 6662 is 44,382,244.

   See the pattern?

1. If the number to be squared is 666662:
2. The square has:

   four 4's (one fewer than
      repeating 6's)   4 4 4 4
Next digits: 38                3 8
four 2's (same as repeating 6's)   2 2 2 2
A final 44                                 4 4

3. So the square of 666662 is 444,438,222,244.