14. Square Using Base 100 Method

When a number is close to 100, use this method for quick squaring.



  •     Find the difference from 100 (how much more or less the number is from 100).

  •      Square the difference and write it in two digits.

  •     Adjust the number:


          If the number is less than 100, subtract the difference from the number.


         If the number is more than 100, add the difference to the number.


Ex 1: 92² = ?



  •     92 is 8 less than 100 - Difference = -8

  •     Square the difference: (−8)2=64

  •     Subtract 8 from 92: 92−8=84

  •     Final answer: 8464


Ex 2: 96² = ?



  • 96 is 4 less than 100 - Difference = -4

  • Square the difference: (−4)2=16

  • Subtract 4 from 96: 96−4=92

  • Final answer: 9216


Ex 3: 107² = ?



  •    107 is 7 more than 100 - Difference = +7

  • Square the difference: (7)2=49

  •     Add 7 to 107: 107+7=114

  •      Final answer: 11449


Why Use This Method ?



  •     Quick calculations for numbers close to 100

  •     No need for long multiplication

  • Saves time in mental math & exams