Find the square of a number (nearing to 100) mentaly


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How much is 5² ? How about 12² ?

Well, if you have already finished the gymnasium then maybe you are already used to find the square for these numbers. But how about 104² ?

I found another useful technique which helps you finding quickly and mentally (no need for pen and paper) the square for any number.

Let’s take 104² 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: 4² = 16

So the answer is: 104² = 10816.

Let’s try 112²:

  • 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: 12²=144

So the answer is: 112² = 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 96² 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 -4² = 16; so the last two digits of our square is 16

The answer is : 96² = 9216

Note: it is very important that the number you choose to square to be nearest 100, otherwise this method is not efficient.

About Eugen Mihailescu

Always looking to learn more about *nix world, about the fundamental concepts of arithmetic, algebra and geometry. I am also passionate about programming, database and systems administration.
This entry was posted in Algebra, Maths and tagged , . Bookmark the permalink.

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