1. Choose a number with an 8 and (at least 3) repeating 3's.
2. The square is made up of:
   • first digits: 69 & two fewer 4's than repeating 3's
   • next digits: 3 & same number of 8's as repeating 3's
   • last digit: 9

   Example:

1. If the number to be squared is 8333:
2. The square has:

   first digits: 60 and two fewer
    4's than 3's                 6 9 4
next digits: 3 and same number of
    8's as 3's                        3 8 8 8
last digit: 9                                 9

3. So 8333 × 8333 = 69,438,889.

   See the pattern?

1. If the number to be squared is 833333:
2. The square has:

   first digits: 69 and two fewer
   4's than 3's             6 9 4 4 4
next digits: 3 and same number of
   8's as 3's                        3 8 8 8 8 8
last digit: 9                                    9

3. So 833333 × 833333 = 694,443,888,889.