1. Choose a number with repeating 6's and a final 1.
2. The square is made up of:
   • one fewer 4 than there are repeating 6's
   • 36
   • two fewer 8's than there are repeating 6's
   • A final 921

   Example:

1. If the number to be squared is 6661:
2. The square has:

   two 4's (one fewer than
      repeating 6's)           4 4
Next digits: 36                    3 6
one 8 (two fewer than repeating 6's)   8
A final 921                              9 2 1

3. So the square of 6661 is 44,368,921.

   See the pattern?

1. If the number to be squared is 666661:
2. The square has:

   four 4's (one fewer than
      repeating 6's)    4 4 4 4
Next digits: 36                 3 6
three 8's                           8 8 8
A final 921                               9 2 1

3. So the square of 666661 is 44,4436,888,921.