The idea of settling can be associated with settling in a new land.
Filing is the process and result of filing . This verb, for its part, refers to what is rooted in a certain place .
For example: “The establishment of the company in the industrial hub must be done in the Production Secretariat” , “The facts show that the establishment on Australian soil was not a good idea for the González family” , “We have to fight against the establishment of those harmful habits in our community.”
The roots in mathematics
In the field of mathematics , the operation that consists of obtaining the root of a figure or a statement is known as establishment. In this way, radicalization is the process that, knowing the index and the radind, allows us 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, we must recognize the parts that make up a radical . The root is the number that, multiplied the number of times indicated by the index, results in the radical.
Calculating the root
Suppose we find a radical that shows the cube root of 8 . We will have the radind ( 8 ) and the index or exponent ( 3 , since it is a cube root). Through the establishment, we reach the root : 2 . This means that 2 cubed ( 2 x 2 x 2 ) is equal to 8 .
As can be seen, establishment is an operation that is the inverse of empowerment : returning to the previous example, we see that by multiplying 2 x 2 x 2 ( 2 cubed ) we arrive at the cube root of 8 .
In mathematics, rooting is the operation that allows us to know the root of a statement or a figure.
Complexity of the filing
Filing is a somewhat particular operation in that it is not very easy to solve if you do not have a calculator or, on the contrary, advanced mathematical skills. While if we see an addition, a subtraction or a multiplication we can proceed to carry them out on a sheet using basic techniques, the multiplication can leave us perplexed since at first glance there seems to be no way to relate its radical with 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 that consists of raising the Euler number , approximately 2.71828 , to the x ) and logarithm (applied to a number in a certain base and is the exponent to which the base must be raised to give said number), concepts that most people do not master and for which a calculator or a computer is almost essential.
Starting from the radiation equation, it can be expressed as e raised to the logarithm of x (the radind) over n (the index). The weak point of this procedure is that it is not useful for negative numbers, since the usual logarithm can only be applied for numbers that go from zero to plus infinity .
Its link with empowerment
Since the establishment is nothing more than a different way of representing a potentiation, the properties of the latter are also fulfilled in the former. The only requirement is that the records be positive. For example:
* the root of a product is equivalent to multiplying the roots of the factors, whenever they exist,
* The root of a fraction can also be expressed as the division of the root of the numerator by that of the denominator;
* the root of a root is equal to multiplying the indices together without altering the radical;
* power of a root is equivalent to raising the radical to the power in question.