Square of a Number Using Vedic Mathematics

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. 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. 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(72) Sign in (optional)
showing 1-10 of 72 comments,   sorted newest to the oldest
shreyyyy
2016-01-08 14:25:12 
hey guys how to find square roots in decimal places? like 2.5, 44.5?

any brilliant here?
(0) (0) Reply
monika sharma
2016-01-21 06:13:49 
find the square of the no. simply by removing the decimals then in ans put the decimals twice before the ans.

for eg 2.5
square of 25=625
now in 2.5 decimal is preceding 1 digit
so in 625  answer will precede 2 digits so final answer will be 6.25
(0) (0) Reply
adi
2015-09-16 14:23:41 
39^2=?
Want answer with above method in steps
If given it will be helpful for me
(0) (0) Reply
somesh
2015-10-27 12:30:42 
Consider the base as 40

39   -1
39   -1
-------
(39-1)  / (-1 x -1)
38   /  1   

since it is to base 40 Multiply only the 38 part with 4 = 152
(38×4) /1
152 / 1

Ans = 1521
(0) (0) Reply
Raj (Senior Maths Expert, careerbless.com)
2015-09-16 17:03:43 
The method explained is suitable if the number is close to a power of 10
(0) (0) Reply
Ashraf
2015-06-08 01:14:17 
Using this method how to find 78^2,82^? can i take 70 and 80 respectively for 10 and 100 as used in that method?
(0) (0) Reply
angel
2015-06-04 06:44:06 
9987^2 = ?
(0) (0) Reply
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 !
(0) (0) Reply
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
(0) (0) Reply
shivam
2015-03-12 11:47:19 
How would you find square of 55 using this method??
(0) (0) Reply
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