Tuesday, 4 March 2014

How to Calculate Square of numbers Easily - Mathematics Tricks

Learn excellent tips and tricks for calculating square of any number. And increase your ability to calculate square of any number that will be useful in Competitive examination.

Ever face problem to calculate square of number that are quite big (say greater than 20). Then finally giving up to use calculator to calculate the square of it, I know this is actually not easy as its looks or its other way around. Is there any way to calculate the square in different way which is faster than conventional way and also much simpler?. The Answer is yes, it’s quite possible.

So let get Started, (I am assuming that you know squares till 20.)
First of all starting from basic, let me ask you this one question

What is a square of number?
The answer is quite simple it’s just multiplication of a number with itself.

We will be starting with the numbers ending with ‘5‘. And extending those concept to calculate other number squares. These tutorial is divided into three part for easy understanding (The following trick you might already know therefore you may skip to Part B of tutorial).

Here I will tell you small trick that helps you to calculate the square of a number that ends with ‘5’. What will be answer if I ask you this following question?

Square of 5 - your answer 25
Square of 15 - your answer 125
Square of 25 - your answer 625
Square of 35 - your answer ……

You might take a while to answer that last question because 35 is quite bigger than that if 25 , so what is the trick to calculate this kind of bigger number. Here is simple steps (all these step can be done only in your mind, if required you can use paper and pen if number are much higher):

1: Firstly divide this ’35’ number into two part i.e. 3 and 5 in your mind. Somewhat like this

2: Now we will directly write the answer using these two part, now for 5 write 25

3: Now with the second part of the number, find its consecutive number and multiply with it to obtained 12 i.e.

4: Now finally join these two number to obtained 1225 i.e.

So we finally obtained our square Yeah! Cheers!

Exercise : 
Now if you have understand the above procedure you can easily calculate square of following number (try to solve it now on paper and don’t use calculator)
45, 85,65,55,95 and 105

Now you finally understand this above trick now is time to extend this trick for other number, here we start with our next part tutorials

Now we will try to calculate square of numbers which are 1 greater than or less than numbers ending with ‘5’ and ‘0’ , i.e. numbers like 26 or 24 in case of 25 and 29 or 31 in case of 30. (Here I am assuming that you already knew squares of numbers ending with zeroes)

To calculate square of 26, add 25 square with 26th odd number starting with 1 i.e.

Here to calculate the 26th odd number the formula used is (2*n-1) here n is nth odd number to be find. Now to calculate square of 24 simply replace ‘+’ sign with ‘-‘sign and do the calculation as given above and nth odd term would be 25th odd number i.e.

Similarly for calculating square of 29 or 31 we apply this simple rules (please calculate 29 and 31 square using above these process for practice). So far we have cover squares of number ending with 1, 4, 5, 6, 9 and 0.

Now for calculating for remaining number that ends with 2, 3, 7 and 8 we apply this following simple rule

Now for calculating square of 27 we add 25 square with 4 times 26 i.e.

Here we are dealing with 1 less and 2 less valued number i.e. 25 and 26. We can also calculate square of 22 with this above trick.

Similarly apply this above concept for obtaining square for number ending with 8 or 3

Exercise : 
Try to calculate 33 with this above concept

So finally we have covered every number, in order to master yourself to calculate fast, you must practice that’s all I can say

Exercise : 
Try to calculate square of these numbers.
41, 52,63,74,85,96,47,58, and 69

Important note for extreme mathematics lover a question may arise in your mind how does the trick work, the answer is yet very simple.
Its based on the Formula


Thank you for staying till the end and patiently reading all this tricks, hope you enjoyed it immensely and learned a lot from it.

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Drop your comment below if you have anything to say. Always here to help.

16 Discussion

  1. Replies
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  2. Very nicely explained steps but try to upload video of this.
    video of these tricks will make it more clear.
    thank you:

  3. was easy to understand ...great trick !!explained really good!

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  6. Another Symple Way

  7. how can we square 54163 easily please any one explain..

  8. https://youtu.be/u7MroMiXU5E
    Easy way to find squaring numbers

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