Square of a Number Using Vedic Mathematics

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There are many ways with which we can find out square of a number within seconds. Let’s see how we can find out square of a number faster using Vedic Mathematics (Nikhilam method)

Example 1: Find out the square of 12

Step 1

We need to take the nearest power of 10. So here 10 is the nearest power of 10 which we can take as our base. The deviation to the base = 12-10 = 2

(To find out the deviation, just remove the left most digit "1" and you will get it quickly)

Now the Left Hand Side of the answer (LHS) will be the sum of the number and deviation. Hence the Left Hand Side of the answer (LHS) = 12 + 2 = 14

Step 2

Our base is 10 which has a single zero. This means that our Right Hand Side of the answer (RHS) will have a single digit and that can be obtained by taking the square of the deviation.

Hence the Right Hand Side of the answer (RHS) = 2² = 4

Hence the answer  = 144

 

Example 2: Find out the square of 13

Step 1

We need to take the nearest power of 10. So here 10 is the nearest power of 10 which we can take as our base.  The deviation to the base = 13-10 = 3

(To find out the deviation, just remove the left most digit "1" and you will get it quickly)

To find out the deviation, just remove the left most digit "1" and you will get it quickly  

Now the Left Hand Side of the answer (LHS) will be the sum of the number and deviation.Hence the Left Hand Side of the answer (LHS) = 13 + 3= 16

Step 2

Our base is 10 which has a single zero. This means that our Right Hand Side of the answer (RHS) will have a single digit and that can be obtained by taking the square of the deviation.

Hence the Right Hand Side of the answer (RHS) = 3² = 9

Hence the answer  = 169

 

Example 3: Find out the square of 14

Step 1

10 is the nearest power of 10 which we can take as our base.  The deviation to the base = 14-10 = 4

(To find out the deviation, just remove the left most digit "1" and you will get it quickly)

 

To find out the deviation, just remove the left most digit "1" and you will get it quickly

 
Now the Left Hand Side of the answer (LHS) will be the sum of the number and deviation. Hence the Left Hand Side of the answer (LHS) = 14 + 4 = 18

Step 2

Our base is 10 which has a single zero. This means that our Right Hand Side of the answer (RHS) will have a single digit and that can be obtained by taking the square of the deviation.

Hence the Right Hand Side of the answer (RHS) = 4² = 16. However please note that the Right Hand Side of the answer (RHS) can have only a single digit because our base 10 has a only single zero. Hence, from the obtained number 16, we will take R.H.S as 6 and 1 is taken as a carry which we will add to our LHS. Hence LHS becomes 18+1 = 19

Hence the answer = 196

 

Example 4: Find out the square of 106

Step 1

Here 100 is the nearest power of 10 which we can take as our base.  The deviation to the base = 106-100 = 6

(To find out the deviation, just remove the left most digit "1" and you will get it quickly)

 To find out the deviation, just remove the left most digit "1" and you will get it quickly

Now the Left Hand Side of the answer (LHS) will be the sum of the number and deviation. Hence the Left Hand Side of the answer (LHS) = 106 + 6 = 112

Step 2

Our base is 100 which has two zeros. This means that our Right Hand Side of the answer (RHS) will have two digits and that can be obtained by taking the square of the deviation.

Hence the Right Hand Side of the answer (RHS) = 6² = 36.

Hence the answer = 11236

 

Example 5: Find out the square of 112

Step 1

Here 100 is the nearest power of 10 which we can take as our base.  The deviation to the base = 112-100 = 12

(To find out the deviation, just remove the left most digit "1" and you will get it quickly)

To find out the deviation, just remove the left most digit "1" and you will get it quickly

 
Now the Left Hand Side of the answer (LHS) will be the sum of the number and deviation. Hence the Left Hand Side of the answer (LHS) = 112 + 12 = 124

Step 2

Our base is 100 which has two zeros. This means that our Right Hand Side of the answer (RHS) will have two digits and that can be obtained by taking the square of the deviation. Hence the Right Hand Side of the answer (RHS) = 12² = 144. However please note that the Right Hand Side of the answer (RHS) can have only two digits because our base 100 has only two zeros. Hence, from the obtained number 144, we will take R.H.S as 44 and 1 is taken as a carry which we will add to our LHS. Hence LHS becomes 124+1 = 125

Hence the answer = 12544



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Comments(76)


sasi 23 Jan 2015 10:13 AM
225 deviation is 2  25
   
  225-200=25

 25^2=625 

225+25=250

250*2=500

=>500
        625
      --------
      50625
 225 squares 50625
 

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manaswini 15 Oct 2014 1:39 AM
1. 225-100=125
2.225+125=350
3.125^2=15625
4.consider 25 only so your ans will be - xxx25
5. 156+350=506
6.fin ans = 50625
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kaiyur 27 Sep 2014 12:15 PM
22*23=506
5*5    = 25
answer=50625

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sHIVIKA 06 Jun 2014 11:55 AM
SQQUARE OF 154 ??
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pebjit 26 May 2014 8:08 PM
why you guys are fighting : you are using (a+b)2 = a2+b2+2ab 

but the generalized base technique is great . if anyone know the generalized base teq. then pls post............  

392, 592........  this numbers =?? with generalized base technique  
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Nirmalraj 17 Jun 2014 2:58 PM
we take base 50,which is equal to base 100/2;
59-50=9

59+9=68
this 68 is divided by 2 because we take base 50.
so 68/2=34

and we take 9 square =81

the ans is 3481.
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nilanshi mukherjee 23 May 2014 10:04 AM
its very nice
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vikas 16 May 2014 10:43 PM
how to find the square of 25
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jinku 18 Jun 2014 4:34 PM
its easy....1).first take unit digit which is 5. then square it u get 25..

2)again in the 10 th palce of question the face value is 2..

3)n(n+1) u get 2(3)=6.

therefore ans is 625...

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Harshal 16 May 2014 6:44 PM
Hi, I have one more technique  which works on similar method

let say u want to find square of 32

So take square of ( 3 )2= 9
                          (2)2  = 4

then 2*3*2 = 12


Ans  9
 +    12
+       4
------------------
     1024

This way u can find square of any number. The above techinque only works with the first digit is 1 
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