**Filing** is the process and the result of **lay** . This verb, meanwhile, refers to what **has rooting in a certain place** . For example: *“The establishment of the company in the industrial pole must be done in the Ministry of Production”*, *"The facts show that the settlement on Australian soil was not a good idea for the Gonzalez family"*, *“We have to fight against the establishment of these harmful habits in our community”*.

In the field of **math** , is known as filing the **operation** consisting of **get the root** of a figure or a sentence. Thus, the filing is the process that, knowing the index and the radicand, allows to find the root. This will be the figure that, once raised to the index, will result in the radicand.

To understand these concepts, therefore, it is necessary to recognize the parts that form a **radical** . The root is the number that, multiplied by the number of times indicated by the index, results in the radicand.

Suppose we find a radical that shows the **cube root of 8** . We will have the radicand (**8** ) and the index or exponent (**3** , since it is a cubic root). Through the filing, we reach the **root** : **2** . This means that **2 raised to the cube** (**2 x 2 x 2** ) is equal to **8** .

As you can see, filing is an operation that is inverse to the **empowerment** : retaking the previous example, we see that multiplying **2 x 2 x 2** (**2 raised to the cube** ) we arrive at **square root** from **8** .

The filing is a **operation** somewhat particular, in that it is not very easy to solve if you do not have a calculator or, conversely, with advanced skills for mathematics. While if we see a sum, a subtraction or a multiplication we can proceed to make them on a sheet using basic techniques, the filing can leave us perplexed since at first glance there seems to be no way to relate its radicand to the index to obtain a result .

As if that were not enough, the effective way to calculate a root is through the **exponential functions** (the real function of raising **Euler's number** , **2,71828** approximately at **x** ) and **logarithm** (It applies to a number on a given basis and is the exponent to which the base must be raised to give that number), concepts that most people do not master and for which a calculator or a calculator is almost indispensable **computer** .

In the image you can see the two steps to start from expressing it as **and** raised to the logarithm of **x** (the radicand) about **n** (the index). The weak point of said **process** it is not useful for negative numbers, since the usual logarithm can only be applied for numbers ranging from **zero** to ** plus infinite** .

Since filing is nothing other than a different way of representing an empowerment, **properties** of the latter are also met in the first. The only requirement is that the radicand be positive. For example:

*** the root of a product** it is equivalent to multiplying the roots of the factors, provided that they exist,*** the root of a fraction** It can also be expressed as the division of the root of the numerator by that of the denominator;*** the root of a root** it is equal to multiply the indexes among themselves without altering the radicand;*** root power** is equivalent to raising the radicand to the **power** in question.