1. Choose a number with a 7 and repeating 6's.
2. The square is made up of:
   • first digits: 58 & two fewer 7's than repeating 6's
   • next digits: 67 & one fewer 5 than repeating 6's
   • last digit: 6

   Example:

1. If the number to be squared is 7666:
2. The square has:

   first digits: 58 and two fewer
    7's than 6's                5 8 7
next digits: 67 and one fewer
    5 than 6's                        6 7 5 5
last digit: 6                                 6

3. So 7666 × 7666 = 58,767,556.

   See the pattern?

1. If the number to be squared is 766666:
2. The square has:

   first digits: 58 and two fewer
   7's than 6's           5 8 7 7 7
next digits: 67 and one fewer
   5 than 6's                      6 7 5 5 5 5
last digit: 6                                  6

3. So 766666 × 766666 = 587,776,755,556.