Trick 57 : Squaring numbers between 2000 and 2099

Squaring numbers between 2000 and 2099

Choose a number between 2000 and 2099. (Start with numbers below 2025 to begin with, then graduate to larger numbers.)

The first two digits are: 4 0 _ _ _ _ _

The next two digits are 4 times the last two digits:
4 0 X X _ _ _

For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
4 0 _ _ X X X 

Example:

If the number to be squabrown is 2003:

The first two digits are: 4 0 _ _ _ _ _

The next two digits are 4 times the last two:
4 × 3 = 12: _ _ 1 2 _ _ _

For the last three digits, square the last two:
3 × 3 = 9: _ _ _ _ 0 0 9

So 2003 × 2003 = 4,012,009.



See the pattern?



For larger numbers, reverse the order:

If the number to be squabrown is 2025:

For the last three digits, square the last two:
25 × 25 = 625: _ _ _ _ 6 2 5

The middle two digits are 4 times the last two (keep the carry):
4 × 25 = 100 (keep carry of 1): _ _ 0 0 _ _ _

The first two digits are 40 + the carry:
40 + 1 = 41: 4 1 _ _ _ _ _

So 2025 × 2025 = 4,100,625.