How to Speed Square Several Two-Digit Numbers

The art of squaring numbers faster than the conventional method of calculating the square has long been in my interest ever since I read Edward H. Julius' Rapid Math Tricks and Tips. Some of the techniques revealed here, I invented in my teens and I am certain that it is the shortest possible method found on this planet, up to about 70% faster.

Two of several two-digit numbers you can square quickly would be numbers whose tens digit is 5 and numbers whose tens digit is 9. It may take sometime to adapt to these methods of squaring but once you get the hang of the art you'll be off on far to becoming an impressive human calculator. You've got to practice, practice and practice to a perfect speed of reckoning. Resist the calculator and you will become like it.

Squaring Any Two-Digit Number Beginning With 5

To square any two-digit number beginning with 5 (5 as the tens digit) simply think in the following steps:

Step1) Take the ones digit of the number to be squared and add it to the square of 5 (which is 25).
For example: 53²; 5² + 3 = 28(think 25 + 3).

Step 2) Finally, square the ones digit of the number to be squared and append the result, which should be in the form of a two digit number to previously obtained two digit number as in the following:
Using previous example: 53² ; 3² = 09

Finally, recall; 2809 = 2809 which is the answer

For the square of 53

1) Think 25 + 3 = 28
2) Then think 3² = 09
3) Now append the two- digit number obtained in step 2 to the one in step 1.

2809 is the answer.

There you have it in just two steps where else it could have been four to six steps.
This method is also applicable for numbers whose tens digit is 6. However, it may take a
little longer than for numbers whose tens digit is 5.


Squaring Any Two Digit Number Beginning With 9

Step 1) Think 80

Step 2) Double the ones digit of the number to be squared.

Step 3) Add the product to 80.

Step 4) Subtract the ones digit of the number to be squared from 10 and square the difference.

Step 5) Finally, append the two-digit product obtained in step 4 to the two-digits in step
3.

Example:

To find the square of 98, perform the following:

1) Think 80 + (2 x 8) = 96

2) (10 - 8)² = 04