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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)

profileRaj
2015-02-10 09:26:24 
88-100= -12
LHS = 88+(-12) = 76
RHS = (-12)^2 = 144 =  44 (1 goes to LHS and makes it 77)
answer is 7744

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profiledivya
2014-09-02 12:15:23 
super techniques it is easy to solve this thanks
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profileArk Rukhaiyar
2014-08-23 21:05:39 

I really liked careerbless for this fantastic and fascinating tricks. It's supper. I wish that you make your tricks more systematic.

 

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profilemini
2014-06-26 13:19:03 
how to find cube root by vedic maths
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profileKinjal Dhaduk
2014-06-22 16:14:03 
2^22, 2^2, 222, 22^2 which is largest no. of following?
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profileAnand
2014-06-23 21:38:36 
obviously 2^22
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profileDipto
2014-06-22 09:22:22 
you can find any thing from the above mention method friends.

taking 55

deviation is 5^2 = 25

and addition methods we get 55+5 =60

now we multiply with 60 the 5(cause we have 5 in the left end of 55), 60*5= 300

now put according to the above method  300
                                                               25
                                                          ----------
                                                            3025    



if we take 49   

deviation 9 and 9^2 = 81

addition  49+9 = 58

multiply 58* 4 (cause we have 4 in the left side of 49) =232
so  232
         81
-----------------
      2401


***  any thing u can find by this method 


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profileraidul shekh
2014-08-06 16:51:12 
How to find square root of a given number
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profileraju
2014-06-15 21:08:32 
how to find square of 225,154,189????????????????????

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profilesasi
2015-01-23 07:43:29 
225 deviation is 2  25
   
  225-200=25

 25^2=625 

225+25=250

250*2=500

=>500
        625
      --------
      50625
 225 squares 50625
 

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