Product of rational radicals

Perhaps best, before advancing an explanation of the Rational Radical Product, is to take into account certain definitions, necessary to understand this operation within its precise mathematical context.

Product of rational radicals

Fundamental definitions

In this sense, it may also be prudent to delimit this conceptual review to five specific notions: Fractions, Fraction multiplication, radication, Similar Roots and Rational Radicals, as these are expressions and operations directly related to the mathematical procedure by which it determines the product of multiplying two or more rational radicals. Here are each of these concepts:

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Consequently, it will begin by saying that Fractions have been generally explained by Mathematics as a type of expression, by which you realize rational numbers, i.e. that fractions will be used to represent amounts fractional or non-whole. They shall also constitute an expression consisting of two elements, each of which has been described as follows:

  • Numerator: First, the Numerator will be understood as the element that occupies the top of the fraction. It has the mission of pointing out how many parts of the whole represents the fraction.
  • Denominator: For its part, the Denominator will be the second element of the fraction, and will occupy the bottom of it. Your task will be to indicate how many parts the whole is divided, of which the numerator represents only a few, or sometimes each of them.

Multiplication of fractions

In another order of ideas, it will also be prudent to throw lights on the definition of Fraction Multiplication, which can be understood as an operation in which it is a question of determining what product is obtained by adding a fraction by itself, so many times as noted by another expression of this kind, hence some authors consider this procedure as an abbreviated sum of fractions.

As for the correct way in which this type of operation should be resolved, the Mathematics indicates that the value of the numerator of the first fraction should be multiplied by the numerator of the second, and the denominator of the first expression by that of the second. This procedure can be expressed mathematically by talking as follows:


It will also be necessary to stop at the concept of Radiation, which has been explained as a mathematical operation by which it is a question of calculating what is the number, which once raised to the index indicated by the operation, results in the value that the operation originally offered as filing, which causes some sources to point to the establishment also as an inverse way of exposing a Power, since if the procedure were expressed in the terms of it, it would then be said that efforts would be made to achieve the base, which is raised to the exponent (index) results in the power (radicating).

Similar roots

On the other hand, similar Roots will be those radicals (numbers or expressions composed of a coefficient and a file that is enclated by a radical sign and an index) that fully match in terms of the index and the establishment they present. However, Mathematics has pointed out that the similarity relationship will not always be as explicit, so sometimes it will be necessary to simplify or break down into prime factors the number offered as settling, operation this one that can reveal relationships of Similarity.

Rational radicals

Finally, it will also be important to bring to chapter the definition given by the Mathematics on Rational Radicals, numbers consisting of a coefficient that is accompanied by a number that is wrapped by a radical sign and has a rational establishment, is i.e. it has like filing a fraction. The correct way to resolve such operations will be by calculating the root of each of the elements that make up the fraction.

Product of rational radicals

Once we have reviewed each of these concepts, it may be much easier to understand the definition of Product of Rational Radicals, an operation which on the other hand is conceived as the procedure by which it is a question of determining what is the the product of adding a rational radical so many times as indicated by another rational radical, hence this operation is also seen as a shortened sum among rational radicals.

Likewise, the mathematical discipline has indicated the correct way to solve this operation, which must then be governed by the following precepts and steps:

  1. First of all, according to the different sources, in order for two rational radicals to multiply they will not need to be similar, but it will suffice – being this indispensable requirement – that both radicals have equal index.
  2. On the other hand, when solving this type of operation will be required to multiply both the coefficients that accompany the radicals and the fractions that function as those settling of these radicals.

This operation can be expressed mathematically as follows:

Product of rational radicals

Example of Rational Radical Product

However, it may be best, when it comes to completing an explanation about the Rational Radical Product, by exposing an example, that allows us to see in a practical way how each of the steps pointed out by the theory about the correct way in which  this type of operation must be resolved. Here’s the following exercise:

Solve the following multiplication of rational radicals:

Product of rational radicals

When starting the resolution of this operation, it will be found that both elements or factors have radicals that have equal indexes, so the multiplication operation is allowed:

Product of rational radicals


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