Let’s see how we can find square of a number faster using Vedic Mathematics (Nikhilam method)
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 $=144$
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 $=169$
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 $=196$
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 $=11236$
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 $=12544$
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.
(ab)^2 = a^2 / 2ab / b^ 2
In our case -- 99^2= 9^2 / 2. 9. 9/9^2
81/162/81
Now write 1 as it is and add 8 to 162 I.e 170
Again write 0 of 170 and add 17 to remaining 81 we get 98 so complete ans is .... 9801 :)
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