# 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)

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)

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)

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(76)

^{2}= a

^{2}+b

^{2}+2ab

^{2}, 59

^{2}........ this numbers =?? with generalized base technique

59-50=9

59+9=68

this 68 is divided by 2 because we take base 50.

so 68/2=34

and we take 9 square =81

the ans is 3481.

let say u want to find square of 32

So take square of ( 3 )2= 9

(2)2 = 4

then 2*3*2 = 12

Ans 9

+ 12

+ 4

------------------

1024

This way u can find square of any number. The above techinque only works with the first digit is 1

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