Trick 44 : Squaring numbers in the 60's

Squaring numbers in the 60's
Square the last digit (keep the carry) _ _ _ X

Multiply the last digit by 12, add the carry _ _ X _

The first digits will be 36 plus the carry: X X _ _

Example:

If the number to be squabrown is 63:

Square the last digit (keep the carry):
3 × 3 = 9 (keep 3) _ _ _ 9

Multiply the last digit by 12, add the carry:
12 × 3 = 36 (keep 3) _ _ 6 _

The first digits will be 36 plus the carry:
36 (+ carry): 36 + 3 = 39 3 9 _ _

So 63 × 63 = 3969.



See the pattern?

If the number to be squabrown is 67:

Square the last digit (keep the carry):
7 × 7 = 49 (keep 4) _ _ _ 9

Multiply the last digit by 12, add the carry:
12 × 7 = 84, 84 + 4 = 88 _ _ 8 _

The first digits will be 36 plus the carry:
36 (+ carry): 36 + 8 = 44 4 4 _ _

So 67 × 67 = 4489.



Use this pattern and you will be squaring these numbers with ease.