Squaring of a number ending with 5

After you read this article , you would be able to find the answers to the square of numbers ending with 5, almost instantly and mentally.
For example , you squares of 35 , 75 , 95 , 105 etc.
Here's how to do it,

Imagine in mind the number, suppose 35 in your mind to be of two parts "3" and "5" ( If it is difficult for you to imagine , write it at a piece of paper )
Now, multiply the first part of the number with a number that is one ( 1 ) greater than it ( Here, "3" is to be multiplied with "4" as 3 + 1 = 4 ) , this will be the first part of your final answer.
Here, 3 x 4 = 12 , so , 12 will be the first part of your final answer.
Next we know 5²=25 , so 25 will be the next part of your final answer.

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Multiplication with 11

Multiplication with 11 looks difficult, but it is easy too , if you follow this vedic maths technique..
In order to multiply a number from 11 , You have to move from the number's unit's degit to the last digit ( i.e. from the right to left ) . You have to simply put the unit's digit as it is in the final answer, then you have to add the Unit's degit number with the number at Ten's place and put the answer (if the total of the Unit's and Ten's digit goes above 10 then you should place only the unit digit at the answer and carry the carryover Ten's digit of the answer to the next Hundred's digit and so on till you reach the last digit ) .

Theoritically its too difficult for You to understand if you don't love maths ( like 9/10 people ) ....
So, lets take some example, firstly we should take a two digit number like 35
35 x 11 = Put 5 as the unit digit of your final answer
next add "3" and "5" (as we should move in the left direction digit by digit) and put "8" as the Ten's digit of your final answer.
lastly put "3" as the hundredth and last digit of your final answer. ( this is done because you have already dealt with 5 , 5+3 and lastly 3 )
So the final answer is 385
35 x 11 = 385 ( 3 , 3+5 , 5 )

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Sixteen ( 16 ) Sutras of Vedic Mathematics

This are all the Sixteen Sutras or Aphorisms of Vedic Mathematics with their respective meanings. -

Sr No.	Sutras	Meaning
1.	Ekadhikina Purvena	By one more than the previous one
2.	Nikhilam Navatashcaramam Dashatah	All from 9 and the last from 10
3.	Urdhva-Tiryagbyham	Vertically and crosswise
4.	Paraavartya Yojayet	Transpose and adjust
5.	Shunyam Saamyasamuccaye	When the sum is the same that sum is zero.
6.	(Anurupye) Shunyamanyat	If one is in ratio, the other is zero
7.	Sankalana-vyavakalanabhyam	By addition and by subtraction
8.	Puranapuranabyham	By the completion or non-completion
9.	Chalana-Kalanabyham	Differences and Similarities
10.	Yaavadunam	Whatever the extent of its deficiency
11.	Vyashtisamanstih	Part and Whole
12.	Shesanyankena Charamena	The remainders by the last digit
13.	Sopaantyadvayamantyam	The ultimate and twice the penultimate
14.	Ekanyunena Purvena	By one less than the previous one
15.	Gunitasamuchyah	The product of the sum is equal to the sum of the product
16.	Gunakasamuchyah	The factors of the sum is equal to the sum of the factors
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Squaring of a number ending with 1 (one)

This technique works well for squaring number ending with 1. If you multiply the numbers the traditional way you will see why this works.
For example:
     31² =
Firstly, subtract 1 from the number. The number now ends in zero and will be quite easy to square now.
     30² = 900 (3 x 3 x 10 x 10)
This is our sub-total.

Secondly, add together 30 and 31 -- the number we squared plus the number we want to square.
     30 + 31 = 61
Add this to our sub-total, 900, to get 961 (900 + 61) , which becomes the answer.
Note: For the second step you can simply double the number we squared, 30 x 2 and then add 1.

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About Vedic Mathematics

Vedic Mathematics is an ancient knowledge comprising of 16 sutras or aphorisms related to mathematics, check out all the 16 Sutras of Vedic Mathematics. This set of sutras was extracted from the Hindu Vedas which were written around 1500-900 BC. The founder of Vedic Mathematics was Swami Sri Bharati Krishna Tirthaji Maharaja, a Hindu scholar and mathematician.

It is also believed that this knowledge laid down the foundation of algorithm, square roots, algebra, the concept of zero and various methods of calculations. If you master all the Sutras or aphorisms in the vedic mathematics, you can solve any mathematical problem be it - arithmetic, algebra, geometry, or trigonometry and that also ORALLY !!.

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