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(78)


amit singh 15 Mar 2015 7:21 AM
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
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shivam 12 Mar 2015 2:17 PM
How would you find square of 55 using this method??
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shivam jain 04 Apr 2015 9:18 AM
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
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pg18 12 Mar 2015 2:06 PM
How to find out square of 99?
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kranti 05 Mar 2015 11:52 AM
how to get (56)2??
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shivam jain 04 Apr 2015 9:31 AM
find difference first from 25 i.e. 31 and then difference from 50 i.e 6
 now, LHS is 31 and RHS is 36 i.e square of 6
combine the result to get ans 3136 

this trick is used in 38,28,36,26 etc
lets see 38
subtract frm 25 i.e 13 and subtract frm 50 i.e 12
now 13 is LHS and 144 is RHS but the result is 13144 i.e. 1(3+1)44 =1444 
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rajesh 24 Feb 2015 10:49 AM
(38)2 how to get square
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simbhu 04 Mar 2015 8:13 AM
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
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Sweety 23 Feb 2015 8:23 PM
square of 28????
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Sneha 10 Feb 2015 9:56 PM
After reading this I became a sudden lover of Maths!!!😉 thanks a lot for sharing this!!!
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