1. Choose a number with an 8 and repeating 9's (use a mimimum of three 9's).
2. The square is made up of:
   • first digits: 80 & two fewer 9's than repeating 9's in the number
   • next digits: 82 & one fewer 0 than repeating 9's in the number
   • last digit: 1

   Example:

1. If the number to be squared is 8999:
2. The square has:

   first digits: 80 and two fewer
    9's than rep. 9's            8 0 9
next digits: 82 and one fewer
    0 than rep. 9's                   8 2 0 0
last digit: 1                                 1

3. So 8999 × 8999 = 80,982,001.

   See the pattern?

1. If the number to be squared is 899999:
2. The square has:

   first digits: 80 and two fewer
   9's than rep. 9's      8 0 9 9 9
next digits: 82 and one fewer
   0 than rep. 9's                 8 2 0 0 0 0
last digit: 1                                  1

3. So 899999 × 899999 = 809,998,200,001.