Trick 29 : Squaring a 2-digit number ending in 3

Squaring a 2-digit number ending in 3
Take a 2-digit number ending in 3.

The last digit will be _ _ _ 9.

Multiply the first digit by 6: the 2nd number will be
the next to the last digit: _ _ X 9.

Square the first digit and add the number carried from
the previous step: X X _ _.

Example:

If the number is 43, the last digit is _ _ _ 9.

6 × 4 = 24 (six times the first digit): _ _ 4 9.

4 × 4 = 16 (square the first digit), 16 + 2 = 18
(add carry): 1 8 4 9.

So 43 × 43 = 1849.



See the pattern?

For 83 × 83, the last digit is _ _ _ 9.

6 × 8 = 48 (six times the first digit): _ _ 8 9.

8 × 8 = 64 (square the first digit), 64 + 4 = 68
(add carry): 6 8 8 9.

So 83 × 83 = 6889.