Rationalize denominators when there are no sums or subtractions in this

Perhaps best ly, before addressing an explanation of the correct way to proceed in the event of being before a Rationalization of denominators, when it doesn´t raise any additions or subtractions, is to briefly revise 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 focus this conceptual review on three specific notions: Fractions, Establishment and Rationalization of Denominators, as correspondingly constituted the expression and operation directly related to the procedure to be followed when rationalizing a denominator, in which no addition or subtraction operation is present. Here are each of these concepts:


In this way, one can begin by saying that The Mathematics has defined Fractions as a type of expression by which it is aware of fractional or rational numbers. Consequently, a fraction will be the way to represent unaccurate or non-whole quantities. Thus, the mathematical discipline indicates that the fraction will always be composed of two elements, explained in turn as follows:

  • Numerator: First, the Numerator will be the element of the fraction that occupies the top of it. It has the task of representing each of the parts that have been taken.
  • Denominator: on the other hand, the Denominator will occupy the bottom of the fraction, while its mission will be to indicate in how many parts the whole is divided, from which some or all parts have been taken, which will be represented by the numerator.


In another order of ideas, it will also be necessary to pause for a moment to review the definition of Radiation, which has been explained by the different mathematical sources as an operation, the purpose of which will be to determine what the number is, which being raised to the index that the operation originally offers, results in the establishment also exposed by the operation. Consequently, this operation may also be understood as a reverse expression of the Empoweror, since if it were to be expressed in the terms of the Power, the basis would be sought.

Rationalization of denominators

Finally, the Rationalization of denominators will be understood as the mathematical operation by which it seeks to remove from its radicals or roots any numerical element that serves as the denominator of a fraction, which is done in order to be able to simplify or reduce a minor expression a denominator, a procedure that in turn is impossible to perform in case the denominator is a root.

Rationalize a denominator where there are no additions or subtractions

However, the procedure to be followed, if you want to rationalize a denominator, will vary according to this element has some addition or subtraction, or on the contrary doesn´t have it. In the latter case, in reality the simplest of the Denominator Rationalization, it should proceed as follows:

  • It will multiply the denominator by itself, looking to obtain a square, which allows to remove the element of the radical.
  • Likewise, the numerator of the fraction will be multiplied by the radical denominator.

This procedure may be expressed mathematically as follows:

Example of denominator rationalization without additions or subtractions

However, the best way to complete an explanation of the correct way to Rationalize a denominator in which no addition or subtraction operations appear or exist may be through the exposure of an example, which allows us to see how each One of the steps involved in this type of procedure, as can be seen below:

To do this, we proceed to multiply each of the elements of the fraction by the radical denominator that possesses the expression:

Picture: pixabay.com

Rationalize denominators when there are no sums or subtractions in this
Source: Education  
September 30, 2019

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