1. Choose a number with repeating 6's and a final 7.
2. The square is made up of:
   • The same number of 4's as there are digits in the number;
   • One fewer 8;
   • A final 9.

   Example:

1. If the number to be squared is 6667:
2. The square has:

   four 4's (number of digits
   in number)              4 4 4 4
three 8's (one fewer)              8 8 8
a final 9                                9

3. So the square of 6667 is 44448889.

   See the pattern?

1. If the number to be squared is 667:
2. The square has:

   three 4's    4 4 4
two 8's           8 8
a final 9             9

3. So the square of 667 is 444889.