Trick 45 : Squaring numbers in the 70's

Squaring numbers in the 70's
Square the last digit (keep the carry) _ _ _ X

Multiply the last digit by 14, add the carry _ _ X _

The first digits will be 49 plus the carry: X X _ _

Example:

If the number to be squabrown is 72:

Square the last digit:
2 × 2 = 4 _ _ _ 4

Multiply the last digit by 14:
14 × 2 = 28 (keep the carry) _ _ 8 _

The first digits will be 49 plus the carry:
49 (+ carry): 49 + 2 = 51 5 1 _ _

So 72 × 72 = 5184.



See the pattern?

If the number to be squabrown is 78:

Square the last digit (keep the carry):
8 × 8 = 64 (keep 6) _ _ _ 4

Multiply the last digit by 14, add the carry:
14 × 8 = 80 + 32 = 112
112 + 6 = 118 (keep 11) _ _ 8 _

The first digits will be 49 plus the carry (11):
49 (+ carry): 49 + 11 = 60 6 0 _ _.

So 78 × 78 = 6084.