VEDIC MATHS-22

 

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is   blog number 22 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Squaring Numbers"

Squaring Numbers:

Squaring can be defined as 'multiplying a number by itself'.

There are many different ways of squaring numbers. Many of these techniques have their roots in multiplication as squaring is simply a process of Multiplication.

Examples: 

1. (3)^2 is three multiplied by 3 which equals 9
2. (4)^2 is four multiplied by 4 which equals 16

The technique that we will study are:

1. Squaring of numbers using Criss-Cross system.
2. Squaring of numbers using formulae.

(A) Squaring of numbers using Criss-Cross system:

The Urdhva-Tiryak Sutra (the Criss-Cross system) is by far the most popular system of squaring numbers amongst practitioners of Vedic Mathematics. The reason for it's popularity is that it can be used for any type of numbers.

Reference:

We had already learn about "Squaring of numbers using Criss-Cross system." our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-20".

We had already learn about "Squaring of numbers using formulae" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-21".

 

Method:

We see that the two formulae can help us find the squares of any number above and below a round figure respectively. There is another formulae which is used to find the square of numbers, but it is not so popular. I discuss it below.

We know that:

This is Formula that we will be using:

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

Suppose we are asked to find the square of a number. Let us call this number 'a'. Now in the case we will use another number 'b' in such a way that either (a+b) or (a-b) can be easily squared.

Examples:

1.Find the square of 72

In this case, the value of 'a' is 72. Now, we know that

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

Substituting the value 'a' as 72, we can write the above formula as:

(72)^2 = (72+b) (72-b) + b^2

We have substituted the value of 'a' is 72. However, we cannot solve this equation because a variable 'b' is still present. Now, we have to substitute the value of 'b' with such a number that the whole equation become easy to solve.

Then the equation becomes,

(72)^2 = (72+2)*(72-2) + (2)^2

= (74) * (70) + 4

In this case we can find the answer by multiplying 74 by 70 and adding 4 to it. However, if one finds multiplying 74 by 70 difficult, we can simplify it still further. First, multiply 70 by 70 and then 4 by 70 and add both for the answer.

Let us continue the examples given above:

(74)^2 = (70*70) + (4*70) + 4

            = 4900 + 280 + 4

            = 5184

Thus, the square of 72 is 5184.

Answer:

(72)^2 = 5184.

In this example we have taken the value of 'b' as 2. Because of this, the value of (a-b) became 70 and the multiplication procedure become easy (as the number 70 ends with a zero)

2. Find the square of 53

Using the formula a^2 = (a+b)*(a-b) + (b)^2

(53)^2 = (53+b) (53-b) +(b)^2

Now we have to find a suitable value for 'b'. If we take the value of 'b' as 3, the expression (53-3) will be 50 and hence it will simplify the multiplication procedure. So we will take the value of 'b' as 3 and equation will become:

(53)^2 = (53+3) (53-3) +(3)^2

            = (56) (50) + 9

            = (50*50) + (6*50) + 9

            = 2500 + 300 + 9

            = 2809

Thus, the square of 53 is 2809.

Answer:

(53)^2 = 2809.

3. Find the square of 107

In this case example we will take value of 'a' as 107 and take the value of 'b' as 7. The equation becomes:

(107)^2 = (107+7) (107-7) +(7)^2

            = (114) (100) + 49

            = 11400 + 49

            = 11449

Thus, the square of 107 is 11449.

Answer:

(107)^2 = 11449.

4. Find the square of 94

In this case example we will take value of 'a' as 94 and take the value of 'b' as 6. The equation becomes:

(94)^2 = (94+6) (94-6) +(6)^2

            = (100) (88) + 36

            = 8800 + 36

            = 8836

Thus, the square of 94 is 8846.

Answer:

(94)^2 = 8836.

More examples:

1. (82)^2=6724
2. (49)^2=2401
3. (97)^2=9409
4. (199)^2=36601
5. (206)^2=42436

      

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

You may try following example:

1) (12)^2=
2) (98)^2=

3) (102)^2=

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 "Cube Roots of Perfect Cube".     

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I will post my new blog in next week.

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