Subtraction of rational radicals

Perhaps the most convenient, before delving into an explanation of the Rest of Rational Radicals, is to make a conceptual review, which allows to keep in mind some definitions, necessary to understand this operation within its mathematical context Precise.

Fundamental definitions

In this sense, it may also be prudent to delimit this revision to four specific notions: Fractions, Radication, Similar Roots and Rational Radicals, as these are the expressions and operations directly related to the radical backdrop Rational. Here’s how to define each one:


In this way, it will begin by saying that mathematics has defined fractions as one of the possible expressions with which rational numbers count, and in the form of expression that rational numbers have. Consequently, fractions will always serve to represent non-exact or non-whole quantities. Likewise, this discipline has pointed out that fractions are composed of two elements, each of which have been described as follows:

  • Numerator: First, the Numerator will be defined as the number that occupies the top of the expression. Its function is to indicate how many parts of the whole are represented by the fraction.
  • Denominator: On the other hand, the Denominator will occupy the bottom of the fraction, indicating how many parts the whole is divided into.


As for the definition of Radiation, it has been explained in general by the different sources as a type of operation, where it is basically a question of determining what is the number that being raised to the index offered by the operation, results in the stated that this mathematical procedure also originally points out, hence some authors also define the Radicay as an inverse expression to the Empoweror, where if the approach were to be set out in the terms of this latter operation i would then try to determine the basis.

Similar roots

Likewise, it will also be necessary to cast lights on the concept of Similar Roots, which have been conceived by Mathematics as those roots that have the peculiarity of matching both their indexes and their establishments. However, mathematical discipline also points out that not always such roots present this relationship in an obvious way, but that their establishments must be broken down or simplified in order to determine whether they can certainly be classified in this way or not.

Rational radicals

Finally, it will be necessary to be aware of the definition of Rational Radicals, which have been described by the different sources as those expressions that are covered by a radical sign have a rational number or a fraction as in the case. Mathematics also points out that every root of a rational radical must be another root. This operation is solved by calculating the root of each element of the fraction separately.

Subtraction of rational radicals

Once these definitions have been revised, it may be much easier to address the concept of Rational Radical Subtraction, which will be understood as the operation aimed at finding out what the difference is of suppressing the specific amount in a rational radical that has indicated another rational radical.

However, Mathematics points to two important points that need to be met when solving such operations:

  1. First of all, it should be borne in mind that the subtraction of rational radicals is only possible if both minuendo and subtracting have equal establishments and indices, that is, if these are similar roots.
  2. In the second instance, the mathematical discipline indicates that the subtraction will be performed only among the coefficients of the radicals, that is, the number that accompanies the one that is enclosed by the radical sign. The difference is calculated and accompanied by the radical common to both factors. If there are any radicals that do not have an explicit coefficient, it will be assumed that the coefficient is equivalent to the unit.

This operation may be represented mathematically as follows:

Example of how to solve a rest a deal of rational radicals

However, percentity the most efficient way to complete an explanation of the correct way to solve an operation involving the subtraction of rational radicals will be through the exposure of an example, which allows to see in a practical way how each of the steps involved in resolving this type of procedure, as can be seen below:

Resolve the following operation:

To do this, the values of the coefficients must then be subtracted, and the same radical for the result must be retained. The operation can be carried out by this consisting of a subtracting and a minuend that have equal radicals, that is, they have similar roots:

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Subtraction of rational radicals
Source: Education  
September 30, 2019

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