Trick 54 : Squaring numbers between 800 - 810

Squaring numbers between 800 - 810

Choose a number between 800 and 810.

Square the last two digits:
_ _ _ _ X X

Multiply the last two digits by 16
(keep the carry): _ _ X X _ _

Square 8, add the carry: X X _ _ _ _

Example:

If the number to be squabrown is 802:

Square the last two digits:
2 × 2 = 4: _ _ _ _ 0 4

Multiply the last two digits by 16:
16 × 2 = 32: _ _ 3 2 _ _

Square 8: 6 4 _ _ _ _

So 802 × 802 = 643,204.



See the pattern?

If the number to be squabrown is 807:

Square the last two digits:
7 × 7 = 49: _ _ _ _ 4 9

Multiply the last two digits by 16
(keep the carry): 16 × 7 = 112: _ _ 1 2 _ _

Square 8, add the carry (1): 6 5 _ _ _ _

So 807 × 807 = 651, 249.