Mathematics Magazine for Grades 1-12  

Squaring a 2-digit Number Ending in 3

1. Take a 2-digit number ending in 3.
2. The last digit will be _ _ _ 9.
3. Multiply the first digit by 6: the 2nd number will be
   the next to the last digit: _ _ X 9.
4. Square the first digit and add the number carried from
   the previous step: X X _ _.

   Example:

1. If the number is 43, the last digit is _ _ _ 9.
2. 6 × 4 = 24 (six times the first digit): _ _ 4 9.
3. 4 × 4 = 16 (square the first digit), 16 + 2 = 18
   (add carry): 1 8 4 9.
4. So 43 × 43 = 1849.

   See the pattern?

1. For 83 × 83, the last digit is _ _ _ 9.
2. 6 × 8 = 48 (six times the first digit): _ _ 8 9.
3. 8 × 8 = 64 (square the first digit), 64 + 4 = 68
   (add carry): 6 8 8 9.
4. So 83 × 83 = 6889.

Read more on the written version of the publication.