1. Choose a number with a 5 and repeating 9's.
2. The square is made up of:
   • first digits: 35 & two fewer 9's than repeating 9's
   • next digits: 88 & one fewer 0 than repeating 9's
   • last digit: 1

   Example:

1. If the number to be squared is 5999:
2. The square has:

   first digits: 35 and two fewer
    9's than 9's                 3 5 9
next digits: 88 and one fewer
    0 than 9's                        8 8 0 0
last digit: 1                                 1

3. So 5999 × 5999 = 35,988,001.

   See the pattern?

1. If the number to be squared is 599999:
2. The square has:

   first digits: 35 and two fewer
   9's than 9's           3 5 9 9 9
next digits: 88 and one fewer
   0 than 9's                      8 8 0 0 0 0
last digit: 1                                  1

3. So 599999 × 599999 = 359,998,800,001.