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Square of a Number Using Vedic Mathematics

Let’s see how we can find square of a number faster using Vedic Mathematics (Nikhilam method)

Example 1: Find square of $12$

Step 1

$10$ is the nearest power of $10$ which can be taken as our base. The deviation to our base $=12-10=2$ (To find the deviation, just remove the leftmost digit "$1$" and you will get it quickly)

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer $=12+2=14$

Step 2

Our base $10$ has a single zero. Therefore, right side of the answer has a single digit and that can be obtained by taking the square of the deviation.

Hence, right side of the answer $=2^2=4$

Therefore, answer $=144$

Example 2: Find square of $13$

Step 1

$10$ is the nearest power of $10$ which can be taken as our base. The deviation to our base $=13-10=3$ (To find the deviation, just remove the leftmost digit "$1$" and you will get it quickly)

To find the deviation, just remove the leftmost digit

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer $=13+3=16$

Step 2

Our base $10$ has a single zero. Therefore, right side of the answer has a single digit and that can be obtained by taking the square of the deviation.

Hence, right side of the answer $=3^2=9$

Therefore, answer $=169$

Example 3: Find square of $14$

Step 1

$10$ is the nearest power of $10$ which can be taken as our base. The deviation to our base $=14-10=4$ (To find the deviation, just remove the leftmost digit "$1$" and you will get it quickly)

To find the deviation, just remove the leftmost digit

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer $=14+4=18$

Step 2

Our base $10$ has a single zero. Therefore, right side of the answer has a single digit and that can be obtained by taking the square of the deviation.

Hence, right side of the answer $=4^2=16.$ But right side of the answer can have only a single digit because our base $10$ has a only single zero. Hence, from the obtained number $16,$ we will take right side as $6$ and $1$ is taken as a carry which will be added to our left side. Hence left side becomes $18+1=19$

Therefore, answer $=196$

Example 4: Find square of $106$

Step 1

$100$ is the nearest power of $10$ which can be taken as our base. The deviation to our base $=106-100=6$ (To find the deviation, just remove the leftmost digit "$1$" and you will get it quickly)

To find the deviation, just remove the leftmost digit

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer $=106+6=112$

Step 2

Our base $100$ has two zeros. Therefore, right side of the answer has two digits and that can be obtained by taking the square of the deviation.

Hence, right side of the answer $=6^2=36$

Therefore, answer $=11236$

Example 5: Find square of $112$

Step 1

$100$ is the nearest power of $10$ which can be taken as our base. The deviation to our base $=112-100=12$ (To find the deviation, just remove the leftmost digit "$1$" and you will get it quickly)

To find the deviation, just remove the leftmost digit

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer $=112+12=124$

Step 2

Our base $100$ has two zeros. Therefore, right side of the answer has two digits and that can be obtained by taking the square of the deviation.

Hence, right side of the answer $=12^2=144.$ But right side of the answer can have only two digits because our base $100$ has only two zeros. Hence, from the obtained number $144,$ we will take right side as $44$ and $1$ is taken as a carry which will be added to our left side. Hence left side becomes $124+1=125$

Therefore, answer $=12544$

Video Tutorial

Note

This method is extremely useful for competitive examinations and if practiced well, square of a number can be determined within seconds using the same.

Comments(77)

profilemanaswini
2014-10-14 23:09:04 
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
like 0 dislike 0
profilekaiyur
2014-09-27 09:45:05 
22*23=506
5*5    = 25
answer=50625

like 0 dislike 0
profilesHIVIKA
2014-06-06 09:25:47 
SQQUARE OF 154 ??
like 0 dislike 0 reply
profilepebjit
2014-05-26 17:38:40 
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  
like 0 dislike 0 reply
profileNirmalraj
2014-06-17 12:28:36 
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.
like 0 dislike 0
profilevikas
2014-05-16 20:13:05 
how to find the square of 25
like 0 dislike 0 reply
profilejinku
2014-06-18 14:04:42 
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...

like 0 dislike 0
profileHarshal
2014-05-16 16:14:50 
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 
like 0 dislike 0 reply
profileshriram
2014-05-05 20:40:49 
how to find for 26
like 0 dislike 0 reply
profileDeepak
2014-04-15 10:35:47 
How to remove square of 36
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