How to Square Numbers Ending in 5


This tutorial is the first among the series of tutorials on Mathematical shortcuts. In this tutorial, we are going to learn how to obtain the square of a number ending with 5.

For example, numbers such as 25, 35, 95, 115 etc. Lets say, we want to calculate the square of 25.

The entire steps are illustrated in the following figure.

Square_5

 

Step 1 :  Break the number such that 5 i  s on the right and the rest of the digit ( i.e., 2 in this case) is on the left.

square_50

Step 2 :  Obtain the square of 5 which is 25. This forms the RHS part of the answer.

Step 3 :  Take the rest of the digit on the left and multiply by the next higher digit that follows it. In our case, we need to multiply 2 by 3 which gives us 6 which forms the first part of the answer.

So, the final answer is 625.

Similarly, can you compute mentally compute 115?

Square_115

Exercise :  can you mentally obtain the squares of :

  • 125
  • 135
  • 85
  • 95

If you have any doubts regarding this tutorial, please leave a comment or contact me. 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.

10 Comments

    • I am glad you liked it. Thank you so much. Share it with your friends who might find it useful.

  1. Sir,
    It’s really help-full topic but… when apply this rule
    in 625 it doesn’t give me actual result..
    let me clarify.
    625=6(6+1)|25*25
    =42625
    but actual ans is 390625

    • The method is to split the number in two parts : a unit digit and the remaining number ,here 625
      62 and 5
      62*63=3906
      5*5=25
      so answer is 390625

Leave a Reply

Your email address will not be published. Required fields are marked *

Protected by WP Anti Spam