1. Choose a number with a 7 and repeating 9's (use a mimimum of three 9's).
2. The square is made up of:
   • first digits: 63 & two fewer 9's than repeating 9's in the number
   • next digits: 84 & one fewer 0 than repeating 9's in the number
   • last digit: 1

   Example:

1. If the number to be squared is 7999:
2. The square has:

   first digits: 63 and two fewer
    9's than rep. 9's            6 3 9
next digits: 84 and one fewer
    0 than rep. 9's                   8 4 0 0
last digit: 1                                 1

3. So 7999 × 7999 = 63,984,001.

   See the pattern?

1. If the number to be squared is 799999:
2. The square has:

   first digits: 63 and two fewer
   9's than rep. 9's      6 3 9 9 9
next digits: 84 and one fewer
   0 than rep. 9's                 8 4 0 0 0 0
last digit: 1                                  1

3. So 799999 × 799999 = 639,998,400,001.