# 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(44)

^{2}=30

^{2}-30*2+1=841

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; 1

^{2}= 1) to the above answer,

so 29

^{2}= 840 + 1 = 841

Deviation to the base = 253

LHS = 1253 + 253 = 1506

RHS = 253

^{2}= 64009 = 009 (64 is carry) (Because 1000 has 3 zeros and RHS can have only 3 digits)

LHS = 64 + 1506 = 1570

Answer = 1570009

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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