Establishment in whole numbers

Before moving forward on the definition of Radication in whole numbers, it may be best to address the concept of Integers itself, so that we can take into account the nature of the numerical elements on the basis of which this operation arises.


In this sense, one can begin by saying that Mathematics has defined integers as those elements with which all whole and exact quantities can be represented, i.e. within such numbers there is no room for fractional numbers or with decimal expressions.

Set Z

It should also be noted that Whole Numbers are also considered by Mathematics as those numerical elements with which the numerical set, which bears the same name, is constituted, or which is also known as the Z set. However, these numeric elements have a grouping order within this collection, forming subsets and elements that have been described in turn as follows:

  • Positive integers: First, you will find the positive integers, which also make up the set of natural numbers, this collection which is also considered as a subset of Z. These numbers are characterized by being to the right of zero, in the number line, where they extend from 1 to the .
  • Negative integers: Negative integers will constitute another subset of Z. They will be assumed as opposites of negative integers. They will extend from -1 to -o, and will be positioned to the left of zero in the Number line. They must always be annotated in the company of the minus sign (-) with which they differ from the positive number.
  • Zero: Finally, zero will also be an element of natural numbers. However, it will not be considered a number as such, but the absence of quantity. Therefore, since it is not a number, zero will not be considered positive or negative. Similarly, he will consider himself the opposite of himself.

Uses of the Z-set

Likewise, it will be relevant to briefly review each of the mathematical uses in which the different elements for which this set is formed are used, and which will then allow the following mathematical actions:

In this way, thanks to the presence of Positive Integers, the Z set can be used to count elements of a collection, or express accounting amounts.

Likewise, the existence of negative integers within the Z set will allow this collection to be used to express lack or absence of specific quantities.

Finally, the presence of zero in the Z numerical set will be used to signal the total absence of quantity.

Integer establishment

With these definitions in mind, it may be much easier to approach a definition of Integer Establishment, which is understood as a mathematical operation, established on the basis of two integers, which try to determine which is the whole number that has the property that being raised to one of them, results in the other number involved, so this operation is also explained as an inverse form of potentiation.

Elements of the Whole Number Establishment

Referring to each of its respective elements, the Radiation has been described by Mathematics as an operation where three elements can be found:

Index: it will be the number that indicates to the root how many times it must multiply itself, in order to result in the establishment.

Radicando: on the other hand, the Radicando will be the number that should result in the elevation of the root to the number indicated by the Index.

Root: Will be interpreted as a result. Being elevated to the index, it will originate the Radicando.

Example of Integer Establishment

Similarly, the most efficient way to complete an explanation about the Establishment of integers may be through the exposure of an example, where you can see in practice what is the correct way to solve this type of operations, set based on integers, such as the following:

√4 =

In this case, having a file equivalent to 4 and an index equal to 2, being a square root, the root that tries to be calculated must then meet the quality that being raised squared results in the number 4. Therefore you will start searching for numbers that meet this condition:

12 = 1
22 = 4

In doing so, you will quickly find 2 as the number that meets this requirement, so it will be taken as the square root of 4:

√4 = 2      because    22 = 4


Establishment in whole numbers
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Bibliography ► (September 21, 2019). Establishment in whole numbers. Bogotá: E-Cultura Group. Recovered from