Squaring numbers between 2000 and 2099

1. Choose a number between 2000 and 2099. (Start with numbers below 2025 to begin with, then graduate to larger numbers.)
2. The first two digits are: 4 0 _ _ _ _ _
3. The next two digits are 4 times the last two digits:
   4 0 X X _ _ _
4. For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
   4 0 _ _ X X X

   Example:

1. If the number to be squared is 2003:
2. The first two digits are: 4 0 _ _ _ _ _
3. The next two digits are 4 times the last two:
   4 x 3 = 12: _ _ 1 2 _ _ _
4. For the last three digits, square the last two:
   3 x 3 = 9: _ _ _ _ 0 0 9
5. So 2003 x 2003 = 4,012,009.

   See the pattern?

For larger numbers, reverse the order:
1. If the number to be squared is 2025:
2. For the last three digits, square the last two:
   25 x 25 = 625: _ _ _ _ 6 2 5
3. The middle two digits are 4 times the last two (keep the carry):
   4 x 25 = 100 (keep carry of 1): _ _ 0 0 _ _ _
4. The first two digits are 40 + the carry:
   40 + 1 = 41: 4 1 _ _ _ _ _
5. So 2025 x 2025 = 4,100,625.