Square of a Number Using Vedic Mathematics

Take me to Video Tutorial

There are many ways with which we can find out square of a number within seconds. Let’s see how we can find out square of a number faster using Vedic Mathematics (Nikhilam method)

Example 1: Find out the square of 12

Step 1

We need to take the nearest power of 10. So here 10 is the nearest power of 10 which we can take as our base. The deviation to the base = 12-10 = 2

(To find out the deviation, just remove the left most digit "1" and you will get it quickly)

Now the Left Hand Side of the answer (LHS) will be the sum of the number and deviation. Hence the Left Hand Side of the answer (LHS) = 12 + 2 = 14

Step 2

Our base is 10 which has a single zero. This means that our Right Hand Side of the answer (RHS) will have a single digit and that can be obtained by taking the square of the deviation.

Hence the Right Hand Side of the answer (RHS) = 2² = 4

Hence the answer  = 144

 

Example 2: Find out the square of 13

Step 1

We need to take the nearest power of 10. So here 10 is the nearest power of 10 which we can take as our base.  The deviation to the base = 13-10 = 3

(To find out the deviation, just remove the left most digit "1" and you will get it quickly)

To find out the deviation, just remove the left most digit "1" and you will get it quickly  

Now the Left Hand Side of the answer (LHS) will be the sum of the number and deviation.Hence the Left Hand Side of the answer (LHS) = 13 + 3= 16

Step 2

Our base is 10 which has a single zero. This means that our Right Hand Side of the answer (RHS) will have a single digit and that can be obtained by taking the square of the deviation.

Hence the Right Hand Side of the answer (RHS) = 3² = 9

Hence the answer  = 169

 

Example 3: Find out the square of 14

Step 1

10 is the nearest power of 10 which we can take as our base.  The deviation to the base = 14-10 = 4

(To find out the deviation, just remove the left most digit "1" and you will get it quickly)

 

To find out the deviation, just remove the left most digit "1" and you will get it quickly

 
Now the Left Hand Side of the answer (LHS) will be the sum of the number and deviation. Hence the Left Hand Side of the answer (LHS) = 14 + 4 = 18

Step 2

Our base is 10 which has a single zero. This means that our Right Hand Side of the answer (RHS) will have a single digit and that can be obtained by taking the square of the deviation.

Hence the Right Hand Side of the answer (RHS) = 4² = 16. However please note that the Right Hand Side of the answer (RHS) can have only a single digit because our base 10 has a only single zero. Hence, from the obtained number 16, we will take R.H.S as 6 and 1 is taken as a carry which we will add to our LHS. Hence LHS becomes 18+1 = 19

Hence the answer = 196

 

Example 4: Find out the square of 106

Step 1

Here 100 is the nearest power of 10 which we can take as our base.  The deviation to the base = 106-100 = 6

(To find out the deviation, just remove the left most digit "1" and you will get it quickly)

 To find out the deviation, just remove the left most digit "1" and you will get it quickly

Now the Left Hand Side of the answer (LHS) will be the sum of the number and deviation. Hence the Left Hand Side of the answer (LHS) = 106 + 6 = 112

Step 2

Our base is 100 which has two zeros. This means that our Right Hand Side of the answer (RHS) will have two digits and that can be obtained by taking the square of the deviation.

Hence the Right Hand Side of the answer (RHS) = 6² = 36.

Hence the answer = 11236

 

Example 5: Find out the square of 112

Step 1

Here 100 is the nearest power of 10 which we can take as our base.  The deviation to the base = 112-100 = 12

(To find out the deviation, just remove the left most digit "1" and you will get it quickly)

To find out the deviation, just remove the left most digit "1" and you will get it quickly

 
Now the Left Hand Side of the answer (LHS) will be the sum of the number and deviation. Hence the Left Hand Side of the answer (LHS) = 112 + 12 = 124

Step 2

Our base is 100 which has two zeros. This means that our Right Hand Side of the answer (RHS) will have two digits and that can be obtained by taking the square of the deviation. Hence the Right Hand Side of the answer (RHS) = 12² = 144. However please note that the Right Hand Side of the answer (RHS) can have only two digits because our base 100 has only two zeros. Hence, from the obtained number 144, we will take R.H.S as 44 and 1 is taken as a carry which we will add to our LHS. Hence LHS becomes 124+1 = 125

Hence the answer = 12544



Video Tutorial


Comments(63)
Sign in (optional)
showing 11-20 of 63 comments,   sorted newest to the oldest

suraj
2015-07-05 09:56:18 
(38)2=32|2.3.8|82
=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
(0) (0) Reply
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 13 then 144 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
(0) (0) Reply
Sweety
2015-02-23 17:53:47 
square of 28????
(0) (0) Reply
Serge
2015-05-02 02:52:25 
28 + 8 = 36
36 x 2 = 72
8^2 = 64

answer : 720 + 64 = 784
(0) (0) Reply
Sneha
2015-02-10 19:26:42 
After reading this I became a sudden lover of Maths!!!😉 thanks a lot for sharing this!!!
(0) (0) Reply
Vishnu Vijayan
2015-01-31 09:04:56 
How can we find the square of 88 using the above method
(0) (0) Reply
Raj
2015-02-10 09:26:24 
88-100= -12
LHS = 88+(-12) = 76
RHS = (-12)^2 = 144 =  44 (1 goes to LHS and makes it 77)
answer is 7744

(0) (0) Reply
divya
2014-09-02 12:15:23 
super techniques it is easy to solve this thanks
(0) (0) Reply
Ark Rukhaiyar
2014-08-23 21:05:39 

I really liked careerbless for this fantastic and fascinating tricks. It's supper. I wish that you make your tricks more systematic.

 

(0) (0) Reply
mini
2014-06-26 13:19:03 
how to find cube root by vedic maths
(0) (0) Reply
Previous12345 ... 7Next Go
showing 11-20 of 63 comments
Add a new comment ...
Use Discussion Board for posting new aptitude questions.


Name   Email (optional)

10 + 0 = (please answer the simple math question)

Post Your Comment