Sum of rational radicals

Perhaps it may be best to address an explanation of fractional-rooted Sum is to briefly review some definitions, which will allow us to understand this operation in its precise mathematical context.

Fundamental definitions

In this regard, it may also be appropriate to delimit this conceptual revision to four specific notions: Fractions, Roots, Fraction Roots, and Similar Roots, as the expressions and operations directly related to the mathematical procedure, consisting of calculating the total between two or more rational radicals. Here are each of these definitions:


In this way, it will begin by saying that Mathematics has generally explained fractions or rational numbers as a mathematical expression, where it is realized a fractional number, that is, that the fraction is used to represent a non-amount exactly or not whole.

On the other hand, mathematical discipline also points out that fractions are expressed as the quotient between two numbers, which would in turn constitute the elements of the fraction, defined in turn as follows:

  • Numerator: First, you would find the Numerator, which will occupy the top of the fraction, and whose main mission will be to indicate how many parts of the whole represents the fraction.
  • Denominator: in the second instance the Denominator will occupy the bottom of the fraction, having as its mission to target the parts in which the whole is divided, that is, the total parts of which the Numerator points only a few, or sometimes all.


For its part, the Radication can be broadly understood as a mathematical operation, by which it is a question of determining which number raises to the index results in the establishment that initially offers the operation, so some authors have suggested that the Radiation may also be understood as the inverse expression of potentiation, since seen in the terms of the latter operation, it would be sought to determine what the basis of the operation is if the index were the exponent and the filing of the Power.

Roots of fractions

It will also be important to review the definition of Fractionroots, a mathematical operation that can be explained as the procedure for determining the fraction that can serve as the basis, in case the originating operation is raised as a where the index is the exponent and the fraction that serves as the rooting, the power. In simple terms, the root of a fraction will be the trade that counts as rooting a rational number or fraction. The way to resolve it is to calculate the root of each term separately.

Similar roots

Finally, the concept of Similar Roots can be defined as those radicals that have the property of having equal indexes and establishments. Sometimes this relationship is not entirely obvious, so it must be broken down into multiple cousins, or simplified, in order to corroborate whether the radicals can in fact be considered similar or not.

Sum of rational radicals

Once each of these definitions has been revised, an explanation of the Sum of rational radicals can then be delved into, which can basically be understood as an operation in which the values of two or more sums, constituted by roots of fractions, that is, radicals that have rational numbers like rooting.

However, mathematics notes that the sum of rational radicals will not be possible among any kind of fractional roots, but that these radicals must meet the main requirement of being similar radicals, that is, to have equal inthe

Thus, the mathematical discipline will point out that in the sum of rational radicals only the sum of the coefficients of the radicals will be allowed, this being understood as the number that accompanies prior to the radical. Finally, the total obtained will be accompanied by the radical.  This operation may be expressed mathematically as follows:

Example of how to perform a sum of rational radicals

However, it may be that the best way to complete an explanation of the correct way to resolve a sum of rational radicals may be through the presentation of a specific example, which will allow us to see in practice how a operation of this type, as seen below:

Solve the following sum of rational radicals:

To comply with the proposal in the postulate, it will then be necessary to add the coefficients and assume a single radical, since these are similar, because they have equal index and equal radicating:


Sum of rational radicals
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Bibliography ► (September 30, 2019). Sum of rational radicals. Bogotá: E-Cultura Group. Recovered from