1. Choose a number with a 4 and repeating 3's.
2. The square is made up of:
   • first digits: 18 & one fewer 7 than repeating 3's
   • next digits: 4 & one fewer 8 than repeating 3's
   • last digit: 9

   Example:

1. If the number to be squared is 4333:
2. The square has:

   first digits: 18 and one fewer
    7 than 3's                   1 8 7 7
next digits: 4 and one fewer
    8 than 3's                          4 8 8
last digit: 9                                 9

3. So 4333 × 4333 = 18,774,889.

   See the pattern?

1. If the number to be squared is 433333:
2. The square has:

   first digits: 18 and one fewer
   7 than 3's             1 8 7 7 7 7
next digits: 4 and one fewer
   8 than 3's                        4 8 8 8 8
last digit: 9                                  9

3. So 433333 × 433333 = 187,777,488,889.