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)

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(38)

pk 24 Nov 2013 2:16 AM

Is it possible to find out square of any 4 or more digit number using this method

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Jay 24 Nov 2013 9:09 AM

Yes, but this method is easy when the number is close to 10,100,1000, etc

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sri 12 Nov 2013 5:01 AM

nicee111

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Sidhant 06 Nov 2013 7:43 AM

I am very thanks to this site. This is help me to improve my knowledge

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sams 03 Nov 2013 4:33 PM

how to go with the above method to find the square root of 41

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Harish Kumar K V 08 Nov 2013 9:32 AM

41 - 10 = 31 which is RHS(deviation) and LHS is (deviation + number ) 31 + 41 = 72

so square root is 72_

now again find the sqaure root for 31 in the same method

31 - 10 = 21 which is RHS(deviation) and LHS is (deviation + number ) 21 + 31 = 52

so square root is 52_

similarly 21 - 10 = 11 which is RHS(deviation) and LHS is (deviation + number ) 21 + 11 = 32

so square root is 32_

Now sqaure of 11 is 121 but since it is base of 10 take only 1 put in dash(321) and add 12 to 2 of the LHS which is 32

That gives you 2 + 12 = 14 where 1 is carry and gets added to 3 and become 4, so finally square root is 441

Now from here go in the reverse direction

2+44 = 46 with 4 carry added to 5 becomes 96 and square root as 961 for 31

take the last number from 961 which is 1 and put it in 72_ and add 96 to 2 of 72 which gives 96+2 = 98 and carry as 9 which to be added to 7 and 7+9 = 16 combining 1681 is the square of 41

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