VEDIC MATHS-50

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VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 50 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Method of finding Cube The Anupriya Method-1"

Reference:

We had already learn about "Method of cubing number" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-49".

Sometimes the divisors are such that it is difficult to calculate the answer by itself. In these cases, we substitute the divisor using another number and then calculate the answer.

Cubing numbers:
Cubing can be defined as multiplying a number by itself and again by itself.
The cube of a number is expressed by putting a small three on the top right part of the number.
For example, 
3^3 = 9
5^3 = 125.

In this blog we will study two methods of cubing numbers.
  1. Formula Method
  2. The Anupriya sutra 
1. The Anupriya method:

The Anurupya Sutra is based on the formulae that we just studied in previous blog. Have a look at how it works:

(a + b)^3 = (a)^3 + 3 (a^2) b + 3 a (b^2) +(b)^3

The expression on the RHS can be broken into two parts as given below. The first part has the terms a^3, a^2b, ab^2, and b^3 and the second part has the terms 2a^2b and 2ab^2. 

            (a)^3 +   (a^2) b +   a (b^2) + (b)^3

        +              2 (a^2) b + 2 a (b^2)    

         --------------------------------------------------------

           (a)^3 + 3 (a^2) b + 3 a (b^2) + (b)^3        

There is one interesting thing related with this formula is given below:
  • If we take first term (a)^3 and multiply it with b/a gives (a^2)b i.e second term
  • If we take second term (a^2)b and multiply it with b/a gives a(b^2) i.e second term
  • If we take first term a(b^2) and multiply it with b/a gives (b^3) i.e second term
On the basis of the above observations it can be concluded that as we move from right to left the numbers are in geometric progression too and the ratio between them is a/b.

Now look at the second row. You will find that the numbers in the second row are obtained by
multiplying the numbers above them by two. Look at the diagram given below:

             (a)^3 +   (a^2) b +   a (b^2) + (b)^3

                               ⬇️              ⬇️

         +             2 (a^2) b + 2 a (b^2)    

           -----------------------------------------------------

Equal  (a)^3 + 3 (a^2) b + 3 a (b^2) + (b)^3 


The first term of the second row 2a^2b is obtained by multiplying a^2b by 2. The second term 2ab^2 is obtained by multiplying ab^2 by 2.

1. Find the cube of 52  (a = 5, b = 2)

In this case the value of a is 5 and b is 2. We will move from left to right with the ratio of b/a. The value of b/a is 2/ 5

First row:
5^3            = 125
125 *  2/5  =   50 
50   *  2/5  =   20
20   *  2/5  =     8

Second row:
The terms of the second row is obtained by doubling the middle terms of the first row. The final figure is as given below.

                125 |   50 | 20 |  8
                       | 100 | 40 |
             -------------------------------
               125 | 150 | 60 |  8

The final answer is obtained by putting three zeros behind the first term, two zeros behind the second term, one zero behind the third term and no zero behind the last term and adding them.

            125000
              15000
                  600
     +               8
        -----------------
            140608

Answer:
Cube of 52 is 140608.

2. Find the cube of 12  (a = 1, b = 2)

In this case the value of a is 1 and b is 2. We will move from left to right with the ratio of b/a. The value of b/a is 1/ 2

First row:
1^3            =    1
1     *  2/1  =    2 
2     *  2/1  =    4
4   *    2/1  =    8

Second row:
The terms of the second row is obtained by doubling the middle terms of the first row. The final figure is as given below.

                    1 |  2 |   4 | 8
                       |  4 |   8 |
                  ----------------------
                    1 |  6 | 12 | 8

The final answer is obtained by putting three zeros behind the first term, two zeros behind the second term, one zero behind the third term and no zero behind the last term and adding them.

            1000
              600
              120
     +           8
        ------------
            1728

Answer:
Cube of 12 is 1728.


Find Cube of following:

  1. (31)^3 = 29791
  2. (17)^3 =   4913
  3. (14)^3 =   2744 
The simplicity of this method can be vouched from examples given above.


You may try following example:

Find cube of followings

1. (13)^3

2. (27)^3

3. (23)^3

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 "Method of finding Cube The Anupriya Method-2".     


Are you excited for this?...
Then, please wait for it.
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.

Thanks

for giving your valuable time.

Good day😊.

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