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# Vedic Math Sutra: Sutra 5-Sūnyaṁ Samyāsamuccaya

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Sūnyaṁ Samyāsamuccaya: When the sum is the same, that sum is zero

Sūnyaṁ Samyāsamuccaya is a Vedic Math sutra that translates to “When the sum is the same, that sum is zero.” “Sūnyaṁ” refers to zero, which plays a significant role in this sutra.

The principle behind Sūnyaṁ Samyāsamuccaya is that if you have two quantities or expressions with the same sum, you can equate them to zero. This sutra is particularly useful when dealing with equations or balancing equations, as it simplifies calculations by manipulating the given equations.

Here’s an example to illustrate the application of the Sūnyaṁ Samyāsamuccaya sutra.

#### Example

Let’s say you have the equation: 3x + 7 = 4x + 4

To solve this equation, you can apply the Sūnyaṁ Samyāsamuccaya sutra. The idea is to manipulate the equation so that the sum on one side is the same as the sum on the other.

In this case, you want to make the sum on the right side equal to the sum on the left.

To achieve this, you can subtract 3x from both sides of the equation, resulting in the following:

3x – 3x + 7 = 4x – 3x + 4

Simplifying this expression, you get:

0 + 7 = x + 4

Now, according to the Sūnyaṁ Samyāsamuccaya sutra, since the sums on both sides are the same (7 on the left and x + 4 on the right), you can equate them to zero:

7 = x + 4 – 7

By subtracting 7 from both sides, you get:

7 – 7 = x + 4 – 7

Simplifying further:

0 = x – 3

So, the solution to the equation is x = 3.

Using the Sūnyaṁ Samyāsamuccaya sutra, we could simplify the equation and find the value of x without any complex algebraic manipulations.

The Sūnyaṁ Samyāsamuccaya sutra is a powerful tool in Vedic Math that helps solve equations more efficiently, especially when balancing or simplifying expressions.

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