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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

36^{2}

36=50-14

14^{2}=196 TAKE 2 DIGITS AND 1 REMAINING PUT 96 RIGHT SIDE

25-14=11+1 (REMAIN)=12 PUT LEFT SIDE

ANSWER IS 1296

36=50-14

14

25-14=11+1 (REMAIN)=12 PUT LEFT SIDE

ANSWER IS 1296

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thakur arjun singh rajawat

2013-09-20 08:03:11

29^{2}=30^{2}-30*2+1=841

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Deepu

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

so 29^{2} = 840 + 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

so 29

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Jiju

2013-07-21 18:12:18

Base = 1000

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

Deviation to the base = 253

LHS = 1253 + 253 = 1506

RHS = 253

LHS = 64 + 1506 = 1570

Answer = 1570009

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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

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

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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