Vedic Math - Squaring Of Numbers Ending with '5'

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In this article, we shall discuss a very common and interesting trick to square those numbers quickly which are having '5' as last digit. For example, what is the result of 65², 85², 125² ?

Let us start with an example:- 35 x 35. How will you multiply?

The conventional approach is-

     35
   x 35
   -------
    175
   105
 --------
   1225
 --------
 In above problem, we followed the following steps:

1. In first step, we multiply 5 by 35, get 175 and wrote it below the line.
2. In second step, we multiply 3 by 35, get 105, wrote it below the first step and leave one space from right.
3. In last, we add results from both the steps and get 1225 as answer.

Now here is the magical trick or quicker way to do this calculation using Vedic Math (to square any number with a 5 on the end). Let us have a look on the same example once again, following 'Vedic Math' steps to solve it.

1. In 35, the last digit is 5 and other number is 3.
2. Add 1 to the top left digit 3 to make it 4 (i.e. 3+1=4) (See the image below).
3. Then multiply original number '3' with increased number i.e. '4'. Like 3 x 4, and we get 12.
4. Now you can see that this is the left hand side of the answer.
5. Next, we multiply the last digits, i.e 5 x 5 and write down 25 to the right of 12.
6. And here we come up with a desired answer, 1225
7. Visual representation is given below.