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.

Ashraf
2015-06-08 01:14:17
Using this method, how to find $78^2,82^2$ etc. Can I take $70$ and $80$ respectively for $10$ and $100$ as used in that method?
angel
2015-06-04 06:44:06
$9987^2=?$
Siddharth Shankar
2015-11-20 18:03:54
9987 = 10000-13
so, write 9987-13 = 9974 as first four digits from the left.
now (-13)^2 = 169 ; put 0169 after 9974 (0169 because the base has four zeroes in it)

So the answer is: 99740169 !
amit singh
2015-03-15 04:51:36
Hey...

To find square use
(ab)^2 = a^2 / 2ab / b^ 2
For e.g -- 38^2= 3^2 / 2. 3. 8/8^2
9/48/64
Now write 4 as it is and add 6 to 48 I.e 54
Again write 4 of 54 and add 5 to remaining 9 we get 14 so complete ans is .... 1444
shivam
2015-03-12 11:47:19
How would you find square of 55 using this method??
Rajesh
2016-03-13 14:58:27
55^2= 5^2/2.5.5/5^2
25/50/25
Now write 5 as it is and add 2 to 50 i.e become 52 again
write 2 of 52 and add 5 to remaining 25 we get 30 .
Hence answer is : 30 25.
Abcd
2015-05-03 08:57:46
We can use another trick
55^2=first find the square in units place that is 5=25
Now we got the rhs =25
Now we have to find lhs=we have to multiply the number in units place by its ahead number that is 6=5*6=30=lhs
So 55^2=3025
shivam jain
2015-04-04 06:48:51
whenever this type of ques like 55,45,65 etc
use this
1. 55 = 5 , 5
in this unit digit 5 do square which is 25
and , tens digit 5 multiply to the next digit i.e 6=30
now combine the result is 3025
similarly,
45 = 4x5 , 5x5 = 20,25= 2025
pg18
2015-03-12 11:36:15
How to find out square of 99?
Aswin
2015-12-18 18:31:50
100-1=99
99-1=98
Difference from 100 to 99=1
&its square 01
i.e., ans = 9801
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