VEDIC MATHS-106

 

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 106 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Applications of the Sutras & Sub-sutras - 6"

VEDIC MATHEMATIC :

"VEDIC MATHEMATICS" is the name given to the ancient system of mathematics, or, to be precise, a unique technique of calculations based on simple rules and principles, with which any mathematical problem be it arithmetic, algebra, geometry or trigonometry can be solved, hold your breath, orally!

What we call "Vedic Mathematics" is a mathematical elaboration of 'Sixteen Simple Mathematical formulae from the Vedas' as brought out by Sri Bharati Krishna Tirthaji.

Sutras: 

The system is based on 16 Vedic sutras or aphorisms, which are actually word formulae describing natural ways of solving a whole range of problems.

Some examples of sutras are "By one more than the one before", "All from 9 & the last from 10", and "Vertically & Crosswise". These 16 one-line formulae originally written in Sanskrit, which can be easily memorized, enables one to solve long mathematical problems quickly.

11. Yaavadunam ( Whatever the extent of its deficiency )

For the square root of a number close to multiple of 10,
Step 1: Subtract the number by multiple of 10
Step 2: First digit is the subtraction of the number from the result of Step 1
Step 3: the second digit is the square of result from Step 1

Examples:
i. Square of 9 
(9)^2  
= (9-(10-9), (10-9) x (10 – 9))
= 81

ii. Square of 18 
(18)^2
= (18 + 8, 8 x 8)
= 26,64 = 2 (6+6) 4
= 324

iii. Square of 96

(96)^2
96 is 4 below 100, so we reduce 96 by 4, which gives us the first part of answer, 92.
The last part is just (4)^2=16.
= (96 - 4, 4 x 4)
= 92,16 
= 9216

iv. Square of 1006 

(1006)^2

1006 is 6 above 1000, so we add 1006 by 6, which gives us the first part of answer, 1012.

The last part is just (6)^2=36, But with a base 1000 we need 3 figures on the right, so we put 036.

= (1006 + 6, 6 x 6)
= 1012,036 
= 1012016

12. Vyashtisamanstih ( Part and Whole )

Here we look at a neat and easy way of multiplying numbers by using their average.

This come under part and whole or (formula specific General).

Example:

i. Suppose we want to know 29 x 31.

Since the average of 29 and 31 is 30, we might think that 29 x 31 is 30 x 30, or close to it.

In fact 29 x 31 = 899 and this is just 1 below 900.

ii. 28 x 32

Again 30 is their average, 28 x 32 = 896 and this is 4 below 900.

iii. 26 x 34

= (30)^2 - (20)^2

= 900 -16

= 894

iv. 94 x 106

= (100)^2 - (6)^2

= 10000 - 36

= 9964

In next blog we will discuss about "Applications of the Sutras & Sub-sutras - 7".     

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I will post my new blog in next week.

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