How to obtain squares of the numbers from 51 to 59

 

You probably already know the shortcut “how to obtain the square of any 2 digit number”. In this shortcut,  will try to understand the shortcut  how to obtain the squares of the numbers from 51 to 59.  Even though,  you can use the shortcut “how to obtain the square of any 2 digit number” for numbers from 51 to 59, you will see this shortcut will be much faster if you have to obtain the square of the number from 51 to 59.

Mathematical Proof for Squares of the numbers from 51 to 59


Let us understand the algebraic proof behind this shortcut.

Any number from 50 to 59 can be represented as (50+a). Taking the square of this number we have,

 

Square_5059

 

The squares of any 2-digit number would be of the form (25+a)/a2.

Let’s say, we want to obtain the square of 56. The entire steps can be illustrated in the following figure.

Square_56

 

Step 1: First step is to break the number such that you have 6 on the right and 5 on the left side.

Square_56_0

Step 2: Obtain the square of the digit on the right.  So, we have 6 on the RHS. Obtain the square of 6 to get 36. This forms the RHS part of the answer.

Step 3: You have 5 on the LHS. Take the square of it and add the number on the RHS, that is  52 + 6 to get 31. This forms the LHS part of the answer.

So, 562=3136

 

Let’s consider another example. Can you mentally calculate the square of 59. The steps are illustrated in the following figure.

Square_56_2

Try Yourself:


Using this technique, can you obtain the square of:

  • 52
  • 53
  • 57
  • 58

 

If you have any queries regarding this tutorial, please leave a comment. 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.

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