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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.

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
0 0
kaiyur
2014-09-27 09:45:05
22*23=506
5*5    = 25

0 0
sHIVIKA
2014-06-06 09:25:47
SQQUARE OF 154 ??
pebjit
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
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.
0 0
vikas
2014-05-16 20:13:05
how to find the square of 25
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...

0 0
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
shriram
2014-05-05 20:40:49
how to find for 26
Deepak
2014-04-15 10:35:47
How to remove square of 36
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