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December 20, 2013

Vedic Maths Shortcut Technique for Finding Square of a Number

6 comments

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Friends, today we shall discuss a simple vedic math method for multiplications. This method is called "Ekadhikena Purvena" that means by one more than the previous one. In vedic maths there are several methods for multiplication of two numbers. One of the methods explained below is for finding out the square of a number (multiplying a number with the same number) having 5 in the units place.

Example 1 : 35 x 35 = ?

The method explained in the schools gets the answer as shown below.


  • The present method following the sutra "Ekadhikena Purvena" involves the procedure of filling up the blanks.
  • For the problem given above, let us have four blanks (the number of blanks depend on the base of the number).
  • initially, multiply the digits in the units places.
               5 x 5 = 25

  • put the number 25 in the two blanks on RHS (Right Hand Side)

  • Next select one of the two given numbers. That is, select a 35. Pic up the digit that is preceding (purva of) 5, that is 3.
  • Add 1 to 3 (Ekadhika).
               3 + 1 = 4

  • Multiply this 4 with the digit 3 appearing in the second number 35.
              3 x 4 = 12

  • Put this 12 in the two blanks that are on the LHS of the result.

Present status :

Lets do one more problem
45 x 45 = ?
  1. Initially :     5 x 5 = 25
  2. Ekadhika :  4 + 1 = 5
  3. Next :          4 x 5 = 20
  4. Result :       45 x 45 = 20 | 25 = 2025 
Lets try another example
75 x 75 = ?

Result : 5625

Now  you may ask. How to apply this method for three digit numbers ? 
Same process, have a look
115 x 115 = ?

  1. Initially    :   5 x 5 = 25
  2. Ekadhika :  11 + 1 = 12
  3. Next          :  11 x 12 = 132
  4. Result       :  115 x 115 = 132 | 25 = 13225
That's all for now friends. Tomorrow we shall discuss more vedic math shortcut techniques for multiplication. Happy Reading :)



About The Author                                             

Rupali Shete (M.Sc., M.Phil., Ph.D) is a gold medalist from Osmania University (Hyderabad), one of the working members of Rananujan Mathematics Academy and Institute of Scientific Research on Vedas (ISERVE), Currently working in University of Pune.



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6 comments:

  1. for finding square of a number ending with 5 u can use this method for e.g. 35 add 3 with 1 then multiply with that same number i.e. 3*4 =12 multiply with 100 and add 25 (3*4)*100+25 1225

    shared by Krishnananth Saju

    ReplyDelete
  2. Thanks friends. We need more tricks like these..

    ReplyDelete
  3. really very valuable......thanks to gr8ambitionz team for providing valuable material(s)........

    ReplyDelete
    Replies
    1. what about other 2 digits n 3 digits number square

      Delete
  4. nice mam
    bt how to find the squares that are not ending with 5???

    ReplyDelete
  5. square of 123. divide the number with two parts 12 & 3.
    square of 12/2*12*3/square of 3.
    144/72/9
    144+7 29=15129

    ReplyDelete

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