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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)

profileLokendra
2015-09-17 15:11:51 
To find square use 
(ab)^2 = a^2 / 2ab / b^ 2
In our case -- 99^2= 9^2 / 2. 9. 9/9^2
81/162/81
Now write 1 as it is and add 8 to 162 I.e 170
Again write 0 of 170 and add 17 to remaining 81 we get 98 so complete ans is .... 9801 :)
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profilekranti
2015-03-05 09:22:14 
how to get (56)2??
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profileshivam jain
2015-04-04 07:01:08 
find difference first from 25 i.e. 31 and then difference from 50 i.e 6
 now, LHS is 31 and RHS is 36 i.e square of 6
combine the result to get ans 3136 

this trick is used in 38,28,36,26 etc
lets see 38
subtract frm 25 i.e 13 and subtract frm 50 i.e 12
now 13 is LHS and 144 is RHS but the result is 13144 i.e. 1(3+1)44 =1444 
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profilerajesh
2015-02-24 08:19:35 
(38)2 how to get square
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profilesuraj
2015-07-05 09:56:18 
(38)2=32|2.3.8|82
=9|48|64

now come from right
write 4 of 64
4

add 6 to its left i.e 48+6=54
write 4
44

now add 5 to its left i.e 9+5=14
write 14

1444
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profilesimbhu
2015-03-04 05:43:28 
Find minus of 38 from 25 which is 13, then minus of 38 from 50 which is 12.
First two digit is 13 then 144 which square of 12
   answer is 14(1+3)44 = 1444

same as (46)2 is 46 minus 25 is 21 then 50 minus 46 is 4
then answer is 2116. here 16 is square of 4
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profileSweety
2015-02-23 17:53:47 
square of 28????
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profileSerge
2015-05-02 02:52:25 
28 + 8 = 36
36 x 2 = 72
8^2 = 64

answer : 720 + 64 = 784
like 0 dislike 0
profileSneha
2015-02-10 19:26:42 
After reading this I became a sudden lover of Maths!!!😉 thanks a lot for sharing this!!!
like 0 dislike 0 reply
profileVishnu Vijayan
2015-01-31 09:04:56 
How can we find the square of 88 using the above method
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