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.

Raj
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)

divya
2014-09-02 12:15:23
super techniques it is easy to solve this thanks
Ark 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.

mini
2014-06-26 13:19:03
how to find cube root by vedic maths
2014-06-22 16:14:03
2^22, 2^2, 222, 22^2 which is largest no. of following?
Anand
2014-06-23 21:38:36
obviously 2^22
Dipto
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

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

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

sasi
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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