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