Square of a Number Using Vedic Mathematics

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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



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Comments(44)


sonu 29 Jul 2013 1:22 AM
ok thanx
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sonu 22 Jul 2013 1:51 AM
how to find square of 29
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thakur arjun singh rajawat 20 Sep 2013 1:03 AM
292=302-30*2+1=841
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Deepu 23 Jul 2013 1:13 PM
This method is the shortcut for fining squares which are closer to the powers of 10
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saju 31 Jul 2013 3:54 AM
it works for all 2 digits... here the nearest base is 30,

so deviation is 30 - 29 = 1

LHS = base number = 30

RHS  = 29 - deviation = 29 - 1 = 28

LHS * RHS = 30*28 = 840

add square of deviation (ie; 12 = 1) to the above answer,

so 292 = 840 + 1 = 841

 
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venkatesh 21 Jul 2013 1:25 AM
how to find for 1253

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Jiju 21 Jul 2013 11:12 AM
Base = 1000
Deviation to the base = 253
LHS = 1253 + 253 = 1506

RHS = 2532 = 64009 = 009 (64 is carry)  (Because 1000 has 3 zeros and RHS can have only 3 digits)
LHS = 64 + 1506 = 1570
Answer = 1570009
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ganesh 15 Jul 2013 11:13 AM
nice
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shravan 28 Jun 2013 5:08 AM
How to find out the square if the left most digit is not 1???
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Vanga Kishore 12 Jul 2013 2:07 AM
hi...shravan.......for ex to find the squre of  22
by the above process 22 it can be written as 20 and 2
add 2 to the 22 total 24 .up to here ok ....we know that given square number is 22 in this number first digit is 2 so that 24 can be added as two times  result is 48 or multipy with 2 like that coming anwer is 48_ REMAINING DIGIT CAN BE FOUND AS SUARE OF 2 IS 4 ACCORDING GIVEN PROCESS AS ABOVE
THEREFORE THE ANSWER 484
THIS PROCESS CAN BE USED FOR ANY SQURE FOR EX 36
30 AND 6
36+6=42 IT CAN BE MULTPI WITH 3 BECAUSE first digit number is 3 in 36 so that 42*3=126_ and 6*6=36 we want only one digit by carry process result will be 1296
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