1. Choose a number in the 600s (practice with smaller numbers, then progress to larger ones).
2. The first two digits of the square are 36: 3 6 _ _ _ _
3. The next two digits will be 12 times the last 2 digits: _ _ X X _ _
4. The last two places will be the square of the last two digits: _ _ _ _ X X

   Example:

1. If the number to be squared is 607:
2. The first two digits are 36: 3 6 _ _ _ _
3. The next two digits are 12 times the last 2 digits:
   12 × 07 = 84: _ _ 8 4 _ _
4. Square the last 2 digits: 7 × 7 = 49: _ _ _ _ 4 9
5. So 607 × 607 = 368,449.

For larger numbers reverse the steps:
1. If the number to be squared is 625:
2. Square the last two digits (keep carry):
   25x25 = 625 (keep 6): _ _ _ _ 2 5
3. 12 times the last 2 digits + carry:
   12x25 = 250 + 50 = 300 + 6 = 306: _ _ 0 6 _ _
4. 36 + carry: 36 + 3 = 39: 3 9 _ _ _ _
   
5. So 625 × 625 = 390,625.