1. Choose a number with a 2 and repeating 9's.
2. The square is made up of:
   • first digits: 8 & one fewer 9 than repeating 9's
   • next digits: 4 & one fewer 0 than repeating 9's
   • last digit: 1

   Example:

1. If the number to be squared is 2999:
2. The square has:

   first digits: 8 and one fewer
    9 than 9's                      8 9 9
next digits: 4 and one fewer
    0 than 9's                            4 0 0
last digit: 1                                   1

3. So 2999 × 2999 = 8,994,001.

   See the pattern?

1. If the number to be squared is 299999:
2. The square has:

   first digits: 8 and one fewer
   9 than 9's               8 9 9 9 9
next digits: 4 and one fewer
   0 than 9's                        4 0 0 0 0
last digit: 1                                  1

3. So 299999 × 299999 = 89,999,400,001.