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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. Ashok Gupta
2016-08-06 03:23:48
Shortcut method to find the square of any two digit number:

suppose we want to find the square of $96$

$100-96=4$

$96-4/4×4\\ 9216$

$96^2=9216$

lets try another number

$87^2\\ 100-87=13\\ 87-13/13×13\\ 74/169$

$74+1/69\\ 7569$

Now try to square of $46$

$50-4=46$

$\dfrac{46-4}{2}/4×4\\ 21/16\\ 2116$ 0 0 reply Rohit Sharma
2016-07-22 09:57:08
How can we calculate square of $97$ by this method ? 0 0 reply Raj
2016-09-02 21:06:44
Take base $100$

$97-100=-3$
i.e., deviation is $-3$

Left side $=97+(-3)=94$

right side $=(-3)^2=9$
Since base has two zeros, write it as $09$

Hence, answer is $9409$ 0 0 Rajendra Krishna
2016-05-21 05:04:35
What is the method to find out that a number is perfect square or cube ? 0 0 reply shreyyyy
2016-01-08 14:25:12
hey guys how to find square roots in decimal places? like $2.5, 44.5?$
any brilliant here? 0 0 reply Mrugesh
2016-08-09 18:16:49
First of all multiply the number with $100$ and keep that in mind.

Lets take a example of $2.5$
By multiplying it with $100$ it becomes $250$

Now think of the nearest perfect square and that is in this case is $256$

Now find the difference b/w that perfect square and the given no.
the difference b/w $256$ and $250$ is $6$

Now think of the very basic expansion equation $(a-b)^2=a^2-2ab+b^2$
so now in this case, we can say that
$250=(16-x)^2=256-2×16×x+x^2$

Here $x$ is very small. So we can neglect it so.
$6=2×16×x$
So $x=\dfrac{6}{32}$ which is approx $0.1875$
So subtract it from $16$ that makes it $15.8125$

Now remind that we have multiplied the original no. with $100.$ So after rooting we have to divide the answer with $10$
so final answer is $1.58125$ approx.
hope this helps. 0 0 monika sharma
2016-01-21 06:13:49
Find the square of the no. simply by removing the decimals then in ans put the decimals twice before the ans.

for eg $2.5$
square of $25=625$
now in $2.5$ decimal is preceding $1$ digit
so in $625$ answer will precede $2$ digits. So final answer will be $6.25$ 0 0 adi
2015-09-16 14:23:41
$39^2=?$
Want answer with above method in steps.
If given it will be helpful for me 1 0 reply somesh
2015-10-27 12:30:42
Consider the base as $40$

$39\qquad \qquad-1\\ 39\qquad \qquad -1$
-----------------------
$(39-1)~/~(-1×-1)$
$~~38~\qquad /\qquad 1$

Since it is to base $40,$ multiply only the $38$ part with $4$ $=152$
$(38×4)/1$
$152 / 1$

Ans $=1521$ 0 0 Raj
2015-09-16 17:03:43
The method explained is suitable if the number is close to a power of $10$ 0 0
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