1. Choose a number with a 4 and repeating 6's.
2. The square is made up of:
   • first digits: 21 & one fewer 7 than repeating 6's
   • next digits: 1 & one fewer 5 than repeating 6's
   • last digit: 6

   Example:

1. If the number to be squared is 4666:
2. The square has:

   first digits: 21 and one fewer
    7 than 6's                   2 1 7 7
next digits: 1 and one fewer
    5 than 6's                          1 5 5
last digit: 6                                 6

3. So 4666 × 4666 = 21,771,556.

   See the pattern?

1. If the number to be squared is 466666:
2. The square has:

   first digits: 21 and one fewer
   7 than 6's             2 1 7 7 7 7
next digits: 1 and one fewer
   5 than 6's                        1 5 5 5 5
last digit: 6                                  6

3. So 466666 × 466666 = 217,777,155,556.