Trick 41 : Squaring numbers in the 30's

Squaring numbers in the 30's
Square the last digit (keep the carry) _ _ _ X

Multiply the last digit by 6, add the carry _ _ X _

The first digits will be 9 plus the carry: X X _ _


Example:

If the number to be squabrown is 34:

Square the last digit (keep the carry):
4 × 4 = 16 (keep 1) _ _ _ 6

Multiply the last digit by 6, add the carry:
6 × 4 = 24, 24 + 1 = 25 _ _ 5 _

The first digits will be 4 plus the carry:
9 (+ carry): 9 + 2 = 11 1 1 _ _

So 34 × 34 = 1156.



See the pattern?

If the number to be squabrown is 36:

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

Multiply the last digit by 6, add the carry:
6 × 6 = 36, 36 + 3 = 39 (keep 3) _ _ 9 _

The first digits will be 9 plus the carry:
9 (+ carry): 9 + 3 = 12 1 2 _ _.

So 36 × 36 = 1296.



With some practice you will be giving these squares quickly.