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Square of a Number Using Vedic Mathematics

Let’s see how we can find square of a number faster using Vedic Mathematics (Nikhilam method)

Example 1: Find square of $12$

Step 1

$10$ is the nearest power of $10$ which can be taken as our base. The deviation to our base $=12-10=2$ (To find the deviation, just remove the leftmost digit "$1$" and you will get it quickly)

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer $=12+2=14$

Step 2

Our base $10$ has a single zero. Therefore, right side of the answer has a single digit and that can be obtained by taking the square of the deviation.

Hence, right side of the answer $=2^2=4$

Therefore, answer $=144$

Example 2: Find square of $13$

Step 1

$10$ is the nearest power of $10$ which can be taken as our base. The deviation to our base $=13-10=3$ (To find the deviation, just remove the leftmost digit "$1$" and you will get it quickly)

To find the deviation, just remove the leftmost digit

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer $=13+3=16$

Step 2

Our base $10$ has a single zero. Therefore, right side of the answer has a single digit and that can be obtained by taking the square of the deviation.

Hence, right side of the answer $=3^2=9$

Therefore, answer $=169$

Example 3: Find square of $14$

Step 1

$10$ is the nearest power of $10$ which can be taken as our base. The deviation to our base $=14-10=4$ (To find the deviation, just remove the leftmost digit "$1$" and you will get it quickly)

To find the deviation, just remove the leftmost digit

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer $=14+4=18$

Step 2

Our base $10$ has a single zero. Therefore, right side of the answer has a single digit and that can be obtained by taking the square of the deviation.

Hence, right side of the answer $=4^2=16.$ But right side of the answer can have only a single digit because our base $10$ has a only single zero. Hence, from the obtained number $16,$ we will take right side as $6$ and $1$ is taken as a carry which will be added to our left side. Hence left side becomes $18+1=19$

Therefore, answer $=196$

Example 4: Find square of $106$

Step 1

$100$ is the nearest power of $10$ which can be taken as our base. The deviation to our base $=106-100=6$ (To find the deviation, just remove the leftmost digit "$1$" and you will get it quickly)

To find the deviation, just remove the leftmost digit

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer $=106+6=112$

Step 2

Our base $100$ has two zeros. Therefore, right side of the answer has two digits and that can be obtained by taking the square of the deviation.

Hence, right side of the answer $=6^2=36$

Therefore, answer $=11236$

Example 5: Find square of $112$

Step 1

$100$ is the nearest power of $10$ which can be taken as our base. The deviation to our base $=112-100=12$ (To find the deviation, just remove the leftmost digit "$1$" and you will get it quickly)

To find the deviation, just remove the leftmost digit

Left side of the answer is the sum of the number and deviation. Hence, left side of the answer $=112+12=124$

Step 2

Our base $100$ has two zeros. Therefore, right side of the answer has two digits and that can be obtained by taking the square of the deviation.

Hence, right side of the answer $=12^2=144.$ But right side of the answer can have only two digits because our base $100$ has only two zeros. Hence, from the obtained number $144,$ we will take right side as $44$ and $1$ is taken as a carry which will be added to our left side. Hence left side becomes $124+1=125$

Therefore, answer $=12544$

Video Tutorial

Note

This method is extremely useful for competitive examinations and if practiced well, square of a number can be determined within seconds using the same.

Comments(77)

profileTHAKUR ARJUN SINGH RAJAWAT
2013-09-20 07:59:02 
362
36=50-14
142=196 TAKE 2 DIGITS AND 1 REMAINING PUT 96 RIGHT SIDE
25-14=11+1 (REMAIN)=12 PUT LEFT SIDE
ANSWER IS 1296
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profilesonu
2013-07-22 08:51:55 
how to find square of 29
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profilethakur arjun singh rajawat
2013-09-20 08:03:11 
292=302-30*2+1=841
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profileDeepu
2013-07-23 20:13:04 
This method is the shortcut for fining squares which are closer to the powers of 10
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profilesaju
2013-07-31 10:54:09 
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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profilevenkatesh
2013-07-21 08:25:09 
how to find for 1253

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profileJiju
2013-07-21 18:12:18 
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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profileshravan
2013-06-28 12:08:42 
How to find out the square if the left most digit is not 1???
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profileVanga Kishore
2013-07-12 09:07:18 
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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profileasha
2013-06-25 11:00:21 
how to find out the square of two digit number eg;29
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