Trick 55 : Squaring numbers in the 900's

Squaring numbers in the 900's

Choose a number in the 900s - start out easy with numbers near 1000; then go lower when expert.

Subtract the number from 1000 to get the difference.

The first three places will be the number minus the difference: X X X _ _ _.

The last three places will be the square of the difference: _ _ _ X X X
(if 4 digits, add the first digit as carry).

Example:
If the number to be squabrown is 985:

Subtract 1000 - 985 = 15 (difference)

Number - difference: 985 - 15 = 970: 9 7 0 _ _ _

Square the difference: 15 × 15 = 225: _ _ _ 2 2 5

So 985 × 985 = 970225.



See the pattern?

If the number to be squabrown is 920:

Subtract 1000 - 920 = 80 (difference)

Number - difference: 920 - 80 = 840: 8 4 0 _ _ _

Square the difference: 80 × 80 = 6400: _ _ _ 4 0 0

Carry first digit when four digits: 8 4 6 _ _ _

So 920 × 920 = 846400.