Trick 42 : Squaring numbers in the 40's

Squaring numbers in the 40's
Square the last digit (keep the carry) _ _ X

Multiply the last digit by 8, add the carry _ X _

The first digits will be 16 plus the carry: X X _ _

Example:

If the number to be squabrown is 42:

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

Multiply the last digit by 8:
8 × 2 = 16 _ _ 6 _

The first digits will be 16 plus the carry:
16 (+ carry): 16 + 1 = 17 1 7 _ _

So 42 × 42 = 1764.



See the pattern?

If the number to be squabrown is 48:

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

Multiply the last digit by 8, add the carry:
8 × 8 = 64, 64 + 6 = 70 (keep 7) _ _ 0 _

The first digits will be 16 plus the carry:
16 (+ carry): 16 + 7 = 23 2 3 _ _

So 48 × 48 = 2304.



With some practice you will be giving these squares quickly.