Mathematical Shortcut for squaring numbers

 

In this tutorial, we are going to learn the shortcut, how to obtain the square of any 2 digit number or 3-digit numbers.In competitive examinations, we often come across questions where we need to obtain the square of number like  1212, 872 etc.

After practising this shortcut, you will how easy it is to obtain the square of any 2 or 3 digit numbers.  In order to use this shortcut, is important that you know the squares of all the numbers till 30 at least.

I hope you all remember the square formula :  (a + b)2 =  a2 + b2 + 2ab

Let’s modify the formula to look something like this :

Square_numbers_1

 

Let’s understand the steps with an example. Let’s say we want to compute 212.

 

Square_numbers_2

 

 

Step 1 :  Break the number such that a=2, and b=1

Step 2 :  Compute a2, ab and b2 and write as shown in the updated formula

Step 3 :   Notice the second row of the formula is obtained by just repeating the middle term ab of the first row.

Very easy right 🙂

 

Example : Let’s take another example. Let’s say we want to compute  562.  In this a=5 and b=6. Notice the carry-forward in each step.

 

Square_numbers_3

 

Example : Let us consider a 3 – digit number 122. Can you obtain the square of 122 ?

 

Square_numbers_4

 

No matter, how big the number is, as long as you are able to break the numbers in a and b and you know a2 and b2, you can obtain the square of the number very easily.

If you know the squares of all the numbers till 30, it is possible to use the above shortcut to obtain the squares of all the numbers till 300 in under 15 seconds.

 

Exercise : Can you obtain the squares of :

  • 452
  • 782
  • 912
  • 1562
  • 2672

 

Please contact me if some point in the tutorial is not clear. I would be glad to help.

Kiran Chandrashekhar

Hey, Thanks for dropping by. My name is Kiran Chandrashekhar. I am a full-time software freelancer. I love Maths and Mathematical Shortcuts. Numbers fascinate me. I will be posting articles on Mathematical Shortcuts, Software Tips, Programming Tips in this website. I love teaching students preparing for various competitive examinations. Read my complete story.

11 Comments

  1. very nice sir at first the multiplication,squaring,cubing are very difficult for me it takes a lot of time to do that but it became easiest one
    thanks for your sapnaedu sir

  2. thanks a lot sir , very easy formula sir, i l spread to my friends nd needful person, pls give me formula for work-time, train-time-distance on my email sir

  3. It is very very very usefull. It helps me to improve my calculation fast and easy. Thanx sir!!!!!!!!!!!!!

  4. Hi my family member! I want to say that this post is awesome, nice written and include almost all important infos. I’d like to look extra posts like this.

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