13. Squaring Numbers Using Base 50 Method


This method is useful for numbers close to 50.


The steps are similar to the Base 100 method but adjusted for Base 50.



  • Find the difference from 50 (how much more or less the number is from 50).

  • Add/Subtract the difference from 25:


1.  If the number is less than 50, subtract the difference from 25.


2.  If the number is greater than 50, add the difference to 25.



  • Square the difference and write it in two digits.

  • Combine the results to get the final square.


Ex 1: 492



  • 49 is 1 less than 50 -

  •  Difference = -1

  •  Adjust 25: 25−1=24

  •  Square the difference and write it in two digits: (−1)2=01

  •  Combine the results to get the final result : 24 & 01

  •  Ans: 2401


Ex 2: 532



  •  53 is 3 more than 50 - Difference = +3

  •   Adjust 25: 25+3=28

  •   Square the difference and write it in two digits: (3)^2=09

  •   Combine the results to get the final result : 28 & 09

  •    Ans: 2809


Ex 3: 472



  •    47 is 3 less than 50 - Difference = -3

  •     Adjust 25: 25−3=22

  •     Square the difference and write it in two digits: (−3)^2=09

  •    Combine the results to get the final result :  22 & 09

  •     Ans: 2209


Ex 4: 562



  • 56 is 6 more than 50 - Difference = +6

  • Adjust 25: 25+6=31

  • Square the difference and write it in two digits: (6)^2=36

  • Combine the results to get the final result : 31 7 36

  • Ans: 3136


Why Use This Method ?



  •      Quick calculations for numbers near 50

  •       No long multiplication needed

  •      Saves time in mental math & exams