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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.

Lokendra

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 :)

(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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shivam 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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suraj

2015-07-05 09:56:18

(38)^{2}=3^{2}|2.3.8|8^{2}

=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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simbhu

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 1**3** then **1**44 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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Serge

2015-05-02 02:52:25

28 + 8 = 36

36 x 2 = 72

8^2 = 64

answer : 720 + 64 = 784

36 x 2 = 72

8^2 = 64

answer : 720 + 64 = 784

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Sneha

2015-02-10 19:26:42

After reading this I became a sudden lover of Maths!!!😉 thanks a lot for sharing this!!!

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