Root of a radical

Perhaps best case, prior to addressing an explanation of how to correctly calculate the Root of a rational radical, is to pause for a moment in some definitions, which will allow us to understand this operation within its mathematical context.

Fundamental definitions

However, it may also be prudent to delimit this conceptual review to three specific notions: Fractions, Radication, Rational Radical, as these are the expressions and operations directly related to the operation intended to calculate the root of any rational radical. Here are each of these definitions:


In this sense, it will begin to say that Mathematics has explained fractions as one of the two types of mathematical expression, by means of which it is aware of rational or fractional numbers, that is, that fractions are used – mathematically speaking – to express non-whole or non-exact amounts.

Thus, the various sources have pointed out that this expression is composed of two elements, each of which is understood as follows:

  • Numerator: First, the Numerator will be conceived as the numerical element of the fraction, which occupies the top of it, indicating how many parts of the whole have been taken.
  • Denominator: On the other hand, the Denominator can be understood as the element that constitutes the bottom of the fraction. Your mission will be to indicate in how many parts the whole is divided.


With regard to the concept of Radiation, mathematics has indicated that this is understood as a mathematical operation, by which it seeks to determine what is the number, which, being raised to the index originally offered by the operation, results in the it also proposes.

In this way, it can be assumed, as some authors point out, that the Radication is the inverse expression of the Empoweror, since if the Radiation were shown in the terms of the latter it would then be sought the basis.

Rational radicals

Finally, it will be equally relevant to address the definition of Rational Radicals, which have been pointed out by mathematical discipline as a type of radical expression, that is, it has a coefficient and a number enlaced by a radical sign, and whose characteristic is to have a rational number or fraction as settling. In relation to the correct way to resolve such operations, Mathematics states that the root of each element must be calculated separately, which may be expressed as follows:

Root of a rational radical

Once each of these concepts has been revised, it is perhaps certainly much easier to address an explanation of how any operation that proposes as a mission to calculate the root of a rational radical, or in other words, to determine to determine the root of a radical expression that has as a fraction.

In this order of ideas, the Mathematics points out that any such operation will be solved by multiplying the indices of each of the radicals, in order to tuck the fraction with the product of these, a procedure that can be expressed mathematically from the next Way:

Example of how to solve the Root of a Rational Radical

However, perhaps the most efficient way to complete an explanation of how a trade to calculate the Root of a rational radical should be solved is through the exposure of a particular example, which allows us to see in a practical way how follow each of the steps involved in this procedure, as can be seen below:

Resolve the following operation:

To solve this operation, it must then begin by multiplying its different indices, it is necessary to remember that when a radical doesn´t have an explicit index, then it must be assumed that this is equivalent to two, since it is the Root Square:


Root of a radical
Source: Education  
September 30, 2019

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