Find the square of a number (nearing to 100) in head

How much is 5 ² ? How about 12 ² ?

Well, if you have already finished the gymnasium then maybe you are already used to find the square for these numbers. But how about 104 ² ?

I found another useful technique which helps you  square any number in head (no need for pen and paper).

Let's take 104 ² for example:

• add to our number the last digit(s) which are above 100 (I mean 104-100 = 4) : 4 + 104 = 108; so the first digits of our square are 108
• next find the square of the last digit(s) which are above 100 of that number: 4 ² = 16

So the answer is: 104 ² = 10816.

Let's try 112 ²:

• note that we are working in base 100, because 112 is an x + 100.
• add to our number the last digits which are above 100 (I mean 112 - 100 = 12) : 12 + 112 = 124; so the first digits of our square are 124
• next find the square of the last digit(s) which are above 100 of that number: 12 ²=144

So the answer is: 112 ² = 12544.

Note that the 1 and the 4 above should be sum up (which is 5) because we can add to the end just 2 digits (our base 100 has only 2 zeros).

If the number we try to square is below the base (below 100) we use little bit the same technique with some minor differences.

Let's have 96 ² for example:

• because 96 is below our base 100, we find how much our number needs to make 100; 96 - 100 = -4
• add that difference to our number: 96 -4 = 92, so we get the first two digits of our square
• next find the square of that number which is over/under base (in our case under base); this is -4 ² = 16; so the last two digits of our square is 16

The answer is : 96 ² = 9216

Note: although I've said it helps you to square any number in head I must emphasis that it is very important to choose the number to square in head nearest 100, otherwise this method is not efficient.

Now, if you think that this article was interesting don't forget to rate it. It shows me that you care and thus I will continue write about these things.

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Eugen Mihailescu

Founder/programmer/one-man-show at Cubique Software

Always looking to learn more about *nix world, about the fundamental concepts of math, physics, electronics. I am also passionate about programming, database and systems administration. 16+ yrs experience in software development, designing enterprise systems, IT support and troubleshooting.

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