1. Choose a number with repeating 6's and a final 4.
2. The square is made up of:
   • the same number of 4's as repeating 6's
   • 0
   • one fewer 8 than repeating 6's
   • a final 96

   Example:

1. If the number to be squared is 6664:
2. The square has:

   three 4's (same number as
      repeating 6's)           4 4 4
next digit: 38                       0
two 8's (one fewer than repeating 6's) 8 8
a final 96                                 9 6

3. So the square of 6664 is 44,408,896.

   See the pattern?

1. If the number to be squared is 666664:
2. The square has:

   five 4's (same number as
      repeating 6's)   4 4 4 4 4
next digit: 0                    0
four 8's (one fewer than
      repeating 6's)               8 8 8 8
a final 96                                 9 6

3. So the square of 666664 is 444,440,888,896.