How to obtain the squares of the numbers ending in 95?

 

 

This shortcut is really cool. Using this shortcut, you can obtain the squares of any number which ends in 95. For example, numbers such as 195, 295, 595 etc.

Let’s say, we want to calculate the square of 295 i.e., 2952.

The entire steps can be illustrated in the following figure.

 

Square_95

 

Step 1 :  Break the number such that 5 is on the right and the rest of the digits ( i.e, 39 in this case) is on the left.

 

Step 2 :  Obtain the square of 5 on the right to get 025. This forms the second part of the answer. Please note, a number ending with 95 will always have 025 as the last part of the answer when you take its square.

 

Step 3 :  Take the rest of the digits(29) and multiply by 3 which is 1 more than the first digit 2. This forms the LHS part of the answer.

 

Important : The square of any number which ends with a95 would look like a9 x (a+1)/025.

 

Let’s take another example to make it clear. Can you guess, what is the square of 9952 ?

 

Square_95_2

9952 = 99 x (9+1)/025 = 990025.

 

Consider another example: What is 5952 ?

 

Square_95_1

5952 = 59 x (5+1)/025 = 354025.

 

On the similar lines, can you mentally calculate?

  • 6952
  • 8952
  • 3952
  • 6952

 

I hope you find this tutorial useful. Please leave a comment if certain point in the tutorial is not clear.

 

 

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5 Responses to How to obtain the squares of the numbers ending in 95?

  1. Kiran Chandrashekhar says:

    Hi,
    I am glad you like it. Please follow us in facebook for regular updates on new mathematical Shortcuts. Also, share it with your friends, who may find it useful.

  2. Harmeet Singh says:

    Hi Kiran Chandrashekhar ,

    Thanks for sharing this. Its really handy,
    but there is one mistake (Typo may be) in the starting
    you are calculating square of 295, but you have written this on top of it :-
    “Let’s say, we want to calculate the square of 395 i.e., 395^2″.

    Anyway, everything looks fine. :)

  3. suni says:

    your shortcut is very very useful and very interesting to read!

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