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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.
 
 
 

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