Squaring a 2-digit number ending in 2

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

Example:

1. If the number is 52, the last digit is _ _ _ 4.
2. 4 × 5 = 20 (four times the first digit): _ _ 0 4.
3. 5 × 5 = 25 (square the first digit), 25 + 2 = 27 (add carry): 2 7 0 4.
4. So 52 × 52 = 2704.

See the pattern?

1. For 82 × 82, the last digit is _ _ _ 4.
2. 4 × 8 = 32 (four times the first digit): _ _ 2 4.
3. 8 × 8 = 64 (square the first digit), 64 + 3 = 67 (add carry): 6 7 2 4.
4. So 82 × 82 = 6724.

Posted in: Mathematics Tips,Squaring Numbers,Tricky mathematics