Examples of how to solve rational roots

Perhaps the most convenient, prior to addressing each of the examples that will be presented in relation to the calculation of rational roots, is to take into account the definition of Rational Roots, in order to be able to understand each of these exercises in their just mathematical context .

Rational Roots

In this sense, before advancing the concept of Rational Roots, it may be perhaps relevant to first recall the very concept of Radiation, which has been generally described by Mathematics as the operation whose main objective is to determine what is the number, which raises to the index provided by the operation results in the number being enlisted by the radical sign, that is, the filing.

Hence, many authors also choose to explain the Radication as a reverse expression of the Empoweror, since the Root – if the operation was expressed as Potentiation – would be the basis of this.

Consequently, the Rational Roots will be those operations of Radication, where the establishment – that is, the number wrapped by the radical sign – turns out to be a rational number or fraction. That is, this procedure will try to determine what is the fraction, which is raised to the index that the originally provided operation, results in the fraction that meets the filing times.

How to Fix Rational Roots

Likewise, the mathematical discipline has also indicated what should be the correct way in which such operations should be resolved, for which the following steps should be followed:

  1. – Once determined that it is a Rational Root, the root index should be identified.
  2. – Subsequently, the root of each element of the fraction, that is, of the Numerator and Denominator, must be calculated.
  3. – Finally, it will be searched if there is any way to simplify the obtained fraction.

Examples of how to calculate rational roots

However, the most efficient way to study the right way to solve filing operations where the filing is a fraction may be through the exposure of some examples, which will allow to see in a practical way how each of the steps are applied pointed out by mathematics. Here’s each one:

Example 1

Calculate the following rational root:

The first thing to do to resolve this operation will be to determine what the radical index is, which as it is not explicitly expressed will be taken as equal to 2. Having done this, the square root of each of the fraction elements should then be calculated separately:

Once the square root of each element has been determined, and verified that it cannot actually be further simplified, this expression is taken as the response to the exercise.

Example 2

Resolve the following operation:

Similarly, when resolving this operation, the index at which each element of the root is raised must be taken into account. In this case, it is the 3, so the cubic root of both the numerator and the denominator must then be calculated separately:

Being larger amounts, it is best to determine what is the cubic root of each element, it will be to break down these amounts into their prime numbers:

Therefore, you will have the following:

Likewise, seeing that the fraction cannot be simplified much further, this will be taken as the final expression.

Example 3

Resolve the following operation:

In the face of this operation, the first step of determining the root index, which is equal to 2, that is, that it is a square root with rational establishment, will be met. To solve it, as dictated by mathematical theory, the square root of each element must be calculated separately:

Doing so will show that only one of the elements can be taken from the root. So you will choose to leave them expressed in this way.

Other examples

Likewise, the following exercises can be taken as examples of how to solve rational roots:

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Examples of how to solve rational roots
Source: Education  
October 17, 2019

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