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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)

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)

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)

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)

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.

Debdut Mukherjee
2014-01-19 15:36:44
What about the square of 312, 487, 1117, etc.? Will this technique work?
pk
2013-11-24 09:16:01
Is it possible to find out square of any 4 or more digit number using this method
Jay
2013-11-24 16:09:50
Yes, but this method is easy when the number is close to 10,100,1000, etc
0 0
sams
2013-11-03 23:33:43
how to go with the above method to find the square root of 41
Harish Kumar K V
2013-11-08 16:32:34
41 - 10 = 31 which is RHS(deviation) and LHS is (deviation + number ) 31 + 41 = 72
so square root is 72_

now again find the sqaure root for 31 in the same method
31 - 10 = 21 which is RHS(deviation) and LHS is (deviation + number ) 21 + 31 = 52
so square root is 52_

similarly 21 - 10 = 11 which is RHS(deviation) and LHS is (deviation + number ) 21 + 11 = 32
so square root is 32_

Now sqaure of 11 is 121 but since it is base of 10 take only 1 put in dash(321) and add 12 to 2 of the LHS which is 32
That gives you 2 + 12 = 14 where 1 is carry and gets added to 3 and become 4, so finally square root is 441

Now from here go in the reverse direction
2+44 = 46 with 4 carry added to 5 becomes 96 and square root as 961 for 31

take the last number from 961 which is 1 and put it in 72_ and add 96 to 2 of 72 which gives 96+2 = 98 and carry as 9 which to be added to 7 and 7+9 = 16 combining 1681 is the square of 41

0 0
Senthilkumar
2014-03-05 14:05:45
41
41 *
-------
41
164
-------
1681 Ans

isn't that simple?

0 0
jisstpalelil
2014-04-15 07:31:51
U r right senthilkumar, this trick is not much easy 4 such no.
0 0
sweetdreams
2013-09-25 05:03:59
36^2=(3*10)+6

to find rhs: 6^2=36
base has only 1 zero, therefore 3 is a carry

to find lhs: 36+6=126+carry=126+3=129
therefore

result is 1296
Akshay
2013-09-01 13:16:32
I can give alternate method to find of the square of any number

let say 26

RHS= 6^2=36 then right 6 carry 3

middle term 2(2*6)=24+carry i.e. 27 so number is 76 carry 2

LHS= 2^2=4+carry i.e. 4+2=6

sourav
2013-08-05 20:30:35
how to do 36^2