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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)

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)

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)

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)

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.

THAKUR 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
0 0
sonu
2013-07-22 08:51:55
how to find square of 29
thakur arjun singh rajawat
2013-09-20 08:03:11
292=302-30*2+1=841
0 0
Deepu
2013-07-23 20:13:04
This method is the shortcut for fining squares which are closer to the powers of 10
0 0
saju
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
0 0
venkatesh
2013-07-21 08:25:09
how to find for 1253

Jiju
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
0 0
shravan
2013-06-28 12:08:42
How to find out the square if the left most digit is not 1???
Vanga 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
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
0 0
asha
2013-06-25 11:00:21
how to find out the square of two digit number eg;29