Trick 46 : Squaring numbers in the 80's

Squaring numbers in the 80's
Square the last digit (keep the carry) _ _ X

Multiply the last digit by 16, add the carry _ X _

The first digits will be 64 plus the carry: X X _ _

Example:

If the number to be squabrown is 83:

Square the last digit:
3 × 3 = 9 _ _ _ 9

Multiply the last digit by 16:
16 × 3 = 30 + 18 = 48 _ _ 8 _

The first digits will be 64 plus the carry:
64 (+ carry): 64 + 4 = 68 6 8 _ _

So 83 × 83 = 6889.



See the pattern?

If the number to be squabrown is 86:

Square the last digit (keep the carry):
6 × 6 = 36 (keep 3) _ _ _ 6

Multiply the last digit by 16, add the carry:
16 × 6 = 60 + 36 = 96 96 + 3 = 99 (keep 9) _ _ 9 _

The first digits will be 64 plus the carry:
64 (+ carry): 64 + 9 = 73 7 3 _ _

So 86 × 86 = 7396.