# 3. Subsutras of Nikhilam……

Posted January 30, 2009

on:*Let us move towards subsutras of Nikhilam…..*

*1)यावदूनं तवादुनिकृत्य वर्ग च योजयेत |*

*Yavadunam tavadunikrutya varga cha yojayet|*

*Its all about doing squares…..varga means square…..*

It means….Subtract the number (which comes by subtracting that no from base) from the number to be squared…..and take square of that number …….

OOps didnt get anything???…..its difficult to put in words actually….let us understand with examples…….

9^{2 }= (9-1) / 1^{2}

^{ }= 8/1

9 is nearer to base 10…..and one less than so….1 is taken….as we done earlier….also..

Let us understand by solving some more….

6^{2} = (6-4) / 4^{2} = 2/16 = 2+1/6 = 36…..

Recall previous procedures……

7^{2 }= (7-3) / 3^{2} = 49……right????

Now some big ones….

98^{2}= (98-2)/ 2^{2}= 94/04=9404……

Why 0 ???

recall…base 100 so… two zeros..and therefore..2 digits on RHS….

91^{2}= (91-9)/9^{2}= 82/81=8281

999^{2}= (999-2)/ 2^{2} = 998001

990^{2}= (990-10)/10^{2}=980/100=980/100

If u know squares upto 25…you can make squares easily….

or else you always can take….suares taking RHS saperately….

Next….**if number is greater than the base…….**

Its simple….do addition instead of subtraction….

13^{2}= (13+3)/3^{2}

now you do rest…no spoon feeding…..hehhe

Try some more yourself…

*2) एकाधिकेन पुर्वेन|*Ekadhiken Purven|

means add one in rmaining number…by excluding ones place…

But this method is only for some numbers….where 5 comes at ones place..e.g.5, 25, 65, 225….etc

25^{2}= 2(2+1)/5^{2} =2×3=6

995^{2}=99×100/5^{2}= 9900/25=990025…

**note**….here that number of zeros= digits on RHS rule not applicable…

only write LHS and .RHS one after the other….

here u can make 11 x 12 seperate…

115^{2} = 11x(11+1)/5^{2}= 132/25 = 13225….

11:1

12:2

—–

13/2

is it seems to be simple??………….

Now some more examples you practice…..

take suares of……..

85, 993, 14, 75, 91, 1008, 114, 1005, 9998

Dont forget to write comment how was the lesson

with luv….

### 2 Responses to "3. Subsutras of Nikhilam……"

Hi,

This one is great and is really a good post. I think it will help me a lot in the related stuff and is very much useful for me. Very well written I appreciate & must say good job.

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1 | Sweta Joshi

January 30, 2009 at 5:07 pm

Nice Article on Vedic Maths.

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