VEDIC MATHS-58

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 58 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Duplex method"

Vedic maths provides a powerful method to compute the square of any number of any length with ease and get the answer in one line. It uses the concept of ‘dwandwa’ or duplex which is explained in this blog.

The Duplex

As the name suggests, duplex simply means dual or something relating to two. We will be using this concept effectively to find out the squares of different numbers. The role of the duplex is to find the squares of numbers.

We will define a term called ‘dwandwa’ or duplex denoted by ‘D’.

1. Duplex of a single digit is defined as

D(a) = (a)^2

1. D(4) = (4)^2 = 16,
2. D(5) = (5)^2 = 25 etc.

2. Duplex of two digits is defined as

D(ab) = 2(a*b)

1. D(37) = 2(3*7) = 42
2. D(41) = 2(4*1) = 8
3. D(20) = 0

3. Duplex of 3 digits is defined as

D(abc) = 2(a*c) + (b)^2

This can be derived by using D(b) and D(ac) defined above.

We pick up the digits at the two extreme ends i.e ‘a’ and ‘c’ and compute its duplex as 2(a*c).

We then move inwards and pick up the remaining digit ‘b’.

We add the duplex of b i.e. (b)^2 to the result to get the duplex of the 3 digits ‘a’, ‘b’ and ‘c’.

Thus,

1. D(346) = 2(3*6) + 42 = 36 + 16 = 52
2. D(130) = 2(1*0) + 32 = 9
3. D(107) = 2(1*7) + 02 = 14.

4. Duplex of 4 digits is defined as

D(abcd) = 2(a*d) + 2(b*c) = 2 ( ad + bc ) 

Once again, we start from the two digits ‘a’ and ‘d’, compute their duplex as 2(a*d), then move inwards, we get another pair ‘b’ and ‘c’ and compute their duplex as 2(b*c). Thus the final duplex is 2(a*d) + 2(b*c).

1. D(2315) = ( 2(2*5) ) + ( 2(3*1) )  = 20 + 6 = 26
2. D(3102) = ( 2(3*2) ) + ( 2(1*0) )  = 12 + 0 = 12
3. D(5100) = ( 2(5*0) ) + ( 2(1*0) )  = 0

5. Duplex of five digits is defined as

D(abcde) = 2(a*e) + 2(b*d) + (c)^2

1. D(21354) = ( 2×2×4 ) + ( 2×1×5 ) + 32 = 16 + 10 + 9 = 35
2. D(31015) = ( 2×3×5 ) + ( 2×1×1 ) + 02 = 30 +   2 + 0 = 32

Compute the duplex of the following numbers.

1. D(3)        = 09 
2. D(34)      = 24 
3. D(132)    = 13 
4. D(1324)  = 20
5. D(41111) = 11

The simplicity of this method can be vouched from examples given above.

You may try following example:

       

1. D(2) 

2 .D(23) 

3. D(234) 

4. D(2345) 

5. D(23456)

You may answer this in comment box. You may ask your any query or doubt in comment box. I will try to resolve as early as possible.

In next blog we will discuss about "Finding Squares of 2-digit number by the Duplex method".     

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I will post my new blog in next week.

We will meet very soon through our next  blog. Till that stay connected, stay healthy and stay safe.

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