Trick 58 : Squaring numbers between 3000 and 3099

Squaring numbers between 3000 and 3099

Choose a number between 3000 and 3099. (Start with numbers below 3025 to begin with, then graduate to larger numbers.)

The first two digits are: 9 0 _ _ _ _ _

The next two digits are 6 times the last two digits:
9 0 X X _ _ _

For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
9 0 _ _ X X X

Example:

If the number to be squabrown is 3004:

The first two digits are: 9 0 _ _ _ _ _

The next two digits are 6 times the last two:
6 × 4 = 24: _ _ 2 4 _ _ _

For the last three digits, square the last two:
4 × 4 = 16: _ _ _ _ 0 1 6

So 3004 × 3004 = 9,024,016.



See the pattern?



For larger numbers, reverse the order:

If the number to be squabrown is 3025:

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

The middle two digits are 6 times the last two (keep the carry):
6 × 25 = 150 (keep carry of 1): _ _ 5 0 _ _ _

The first two digits are 90 + the carry:
90 + 1 = 91: 9 1 _ _ _ _ _

So 3025 × 3025 = 9,150,625.