VEDIC MATHS-59

 

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 59 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Finding Squares of 2-digit number by the 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’.

Reference:

We had already learn about "Duplex Method" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-58".

Squaring by the Duplex method:

Once the concept of ‘duplex’ is clear, we can compute the square of any number very easily. Let us start with the square of a 2-digit number and then extend it to bigger numbers.

Finding Squares Using the Duplex Method

Two-digit squares :

The square of a 2-digit number ab is defined as 

(ab)^2 = Duplex of ( a | ab | b)

           = D(a) * D(ab) * D(b)

Examples :

1.(57)^2.

Here a = 5 and b = 7.

Step 1 :

• We first find the duplex of 5, which is 25.
• Then we’ll find the duplex of 57 using the formula 2(a*b), which is 2 × 5 × 7 = 70.
• And lastly, we’ll find the duplex of 7, which is (7)^2 or 49.

We write the duplexes like this: 25|70|49

Step 2 :

In this step, we’ll start adding from right to left.

  25|70|49

=  3249

• We put down 9 from 49 and carry over 4 to the next step.
• We then add 70 + 4, which gives us 74. Later, we’ll place 4 down and carry over 7 to the next step
• Finally, we add 25 + 7 (carried over), so this gives us 32.
• Our answer is 3249.

Answer:

(57)^2 = 3249.

2. (74)^2.

Here a = 7 and b = 4.

Step 1 :

We first find out the duplexes of all the digits.

• So the duplex of 7 will be 72, which is 49.
• Next, we’ll find out the duplex of 74 and that is 2 × 7 × 4 = 56.
• Finally, we’ll find the duplex of 4, which is 16.

Now all we have to do is place these duplexes down like this: 49|56|16

Step 2 :

Now in this step, we’ll start adding to get to the final answer. So let’s start from right to left.

• First, we put down 6 from 16 as the first answer digit and then carry over 1 to the next step.
• So 56 + 1 = 57. We now put down 7 as the next answer digit and carry over 5 to the next step.
• So finally, 49 + 5 = 54.

With this, our complete answer is 5476.

Answer:

(74)^2 = 5476.

.Find square of following number by Duplex Method.

1. (32)^2 =   9|  12|  4 = 1024
2. (53)^2 = 25|  30|  9 = 2809
3. (62)^2 = 36|  24|  4 = 3844
4. (88)^2 = 64|128|64 = 7744
5. (96)^2 = 81|108|36 = 9216

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

You may try following example:

       

1. (49)^2

2 .(77)^2 

3. (59)^2

4. (0.34)^2

5. (0.37)^2

In next blog we will discuss about "Finding Squares of 3-digit number by the Duplex method".     

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I will post my new blog in next week.

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