1. Choose a number with repeating 9's and a final 1.
2. The square is made up of:
   • one fewer 9 than there are repeating 9's
   • 82
   • the same number of 0's as there are 9's in the square
   • A final 81

   Example:

1. If the number to be squared is 9991:
2. The square has:

   One fewer 9 than the
   repeating 9's:        9 9
82                           8 2
same number of 0's as 9's
   in the square                 0 0
a final 81                            8 1

3. So 9991 × 9991 = 99820081.

   See the pattern?

1. If the number to be squared is 999991:
2. The square has:

   one fewer 9 than the
   repeating 9's:       9 9 9 9
82                              8 2
same number of 0's as 9's
   in the square                    0 0 0 0
a final 81                                  8 1

3. So 999991 × 999991 = 999982000081.