Examples of how to solve the root of a fraction

Perhaps best lybet, prior to addressing an explanation of how any operation intended to find the root of a rational radical should be resolved, is to briefly review the very definition of this operation, in order to understand each of the exercises within their precise context.

Root of a rational radical

However, in this order of ideas, we should start by remembering that rational radicals have been explained by different mathematical sources such as those root operations that present as settling a fraction, and that must be solved determining which fraction being elevated to the index originally provided by the operation results in the rational expression that functions as filing. Consequently, some authors have pointed out that rational radicals can also be interpreted as the inverse expression of rational base powers.

On the other hand, the Root of a rational radical has been explained, by the different sources as an operation aimed at finding what is the root of a rational radical, that is, what is the fraction that rises to the index pointed to by the general root results in fracci when the root that is enclosed by this main radical is resolved.

Steps to solve the root of a radical

In this sense, Mathematics has also indicated what steps should be taken when solving such an operation, which are basically made up of the following:

  1. First, when faced with a root operation of a rational radical, it is necessary to specify which indexes each root has.
  2. Having done this, we proceed to multiply the values of the indices of each of the radicals present in the operation, in order to convert both radicals into one.
  3. You assume the same establishment.

In this way, the correct way to find a solution for this type of operation can be expressed as follows:

Examples of how to solve the root of a rational radical

However, the most efficient way to approach the study of the roots of a rational radical may be through some examples, which allow us to see in a concrete way the application of each of the steps that must be taken according to the Mathematics to solve this type of operations. Here are some of them:

Example 1

Resolve the following operation:

To resolve this operation, you must start by determining what each radical’s indexes are. In this case they are not explicitly expressed, so it is assumed then that each is equivalent to 2, that is, both are square roots:

Having done this, it will be before a fourth root, so to get the rational expression out of the radical it will be necessary to break down each of its elements into prime factors:

Example 2

To solve the root of a rational radical offered below:

As long as you are facing such an operation, you must start by identifying which indexes are, to multiply them later. In this case it is a square root, that is, with an index equal to 2, and a cubic root, index 3:

Obtained a sixth root, and since you cannot completely remove every element of this radical, if you wanted to express the operation differently, you could choose to change the form of rational radical to that of rational base power, which is done by raising the fraction to a rational exponent:

Other examples

Finally, the following exercises may also be placed as examples of rational radical roots:

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Examples of how to solve the root of a fraction
Source: Education  
October 24, 2019

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