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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.

manaswini

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

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kaiyur

2014-09-27 09:45:05

22*23=506

5*5 = 25

answer=50625

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pebjit

2014-05-26 17:38:40

why you guys are fighting : you are using (a+b)^{2} = a^{2}+b^{2}+2ab

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

39^{2}, 59^{2}........ this numbers =?? with generalized base technique

Nirmalraj

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.

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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jinku

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...

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Harshal

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

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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