1. Choose a number in the 500s (start with low numbers at first; then graduate to larger ones).
2. The first two digits of the square are 25: 2 5 _ _ _ _
3. The next two digits will be 10 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 508:
2. The first two digits are 25: 2 5 _ _ _ _
3. The next two digits are 10 times the last 2 digits:
   10 × 8 = 80: _ _ 8 0 _ _
4. Square the last digit: 8 × 8 = 64: _ _ _ 6 4
5. So 508 × 508 = 258,064.

For larger numbers reverse the steps:
1. Square the last two digits (keep the carry): _ _ _ _ X X
2. 10 times the last two digits + carry: _ _ X X _ _
3. 25 + carry: X X _ _ _ _

   See the pattern?

1. If the number to be squared is 525:
2. Square the last two digits (keep the carry):
   25 × 25 = 625 (keep 6): _ _ _ _ 2 5
3. 10 times the last two digits + carry:
   10 × 25 = 250; 250 + 6 = 256 (keep 2): _ _ 5 6 _ _
4. 25 + carry: 25 + 2 - 27: 2 7 _ _ _ _
5. So 425 × 425 = 275,625.