How to find the square of 245 and other 3-digit numbers from short trick of math?



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Plz note: I have already written an article on how to find the square of any two-digit numbers. The method is similar here but the formula is different and here the formula is a little bit difficult.

Example 1:

Finding (245)2 becomes very simple by applying this below formula or trick of Vedic maths.

(abc)2 = a2 | 2ab | 2ac + b2 | 2bc | c2

In (245)2 we can take values as below.

a = 2
b = 4
c = 5

Putting these values in a2 | 2ab | 2ac + b2 | 2bc | c2 we will get

2 * 2 | 2 * 2 * 4 | 2 * 2 * 5 + 16 | 2 * 4 * 5 | 5 * 5

4 | 16 | 36 | 40 | 25

We can consider 5 columns above starting from | 4 | to | 25 |

If the values inside the columns (other than column first) are greater than or equal to 10 then we will take only the last digit of the value in each column and other digits in that same value will become a "carry" which will be added to the value of the previous column.

So in the last column (5th column) we will take 5 and carry 2 (see outcome below).

We will add the carry 2 to the value in the 4th column > 40 + 2 = 42

Now from the new 4th column value (42) we will take only 2 and carry 4

Again, we will add the carry 4 to the value in the 3rd column > 36 + 4 = 40

Now from the new 3rd column value (40) we will take only 0 and carry 4

Again, we will add the carry 4 to the value in the 2nd column > 16 + 4 = 20

Now from the new 2nd column value (20) we will take only 0 and carry 2

Finally, we will add the carry 2 to the value in the 1st column > 4 + 2 = 6

The result will be as below:

6 | 0 | 0 | 2 | 5 (outcome).

Removing the vertical dashes above we get the answer as 60025.

Let us take another example

Example 2: Suppose we want to know the square of 586.

In (586)2 we can take values as below.

a = 5
b = 8
c = 6

Putting these values in a2 | 2ab | 2ac + b2 | 2bc | c2 we will get

25 | 80 | 60 + 64 | 96 | 36

Now using the carry the outcome will be as below (read from right to left).

25 + 9 (carry)= 34 | 80+ 13 carry=93 |124 + 9 carry= 133 | 96+3 (carry)=99 | 6

the outcome of above will be as below.

34 | 3 | 3 | 9 | 6

Removing the vertical dashes the final answer will be 343396.

Plz note: This Vedic maths method or trick is much easier to find the square of any 3-digit number than doing the usual long multiplication of three digit numbers but you need to remember the formula as mentioned above.

But there is also a great method to find the square of any 3-digit number without using the formula but still very quickly.

There is also one universal method to find the square of any number without worrying whether it is a 2-digit, 3-digit, 4-digit or 5-digit number and it is the easiest and fastest method of all.

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Written by: Rajesh Bihani ( Find me on Google+ )

Disclaimer: The suggestions in the article(wherever applicable) are for informational purposes only. They are not intended as medical or any other type of advice