# Examples of how to add rational roots

Perhaps best lybeh, before setting out some examples of the correct way in which operations involving the sum of rational radicals should be resolved, is to take into account the very definition of this operation, in order to be able to understand these exercises in their precise mathematical context.

In this sense, it should be started by remembering that a rational radical is any operation of Radicación, which has a fraction or rational number as settling, and whose main purpose is to determine then what fraction is that by raising each of its elements to the index originally provided by the operation results in the fraction that it serves the filing times.

It will also be relevant to bring to chapter the definition of Sum of Rational Radicals, which may be understood as a mathematical operation aimed at determining the total of combining the values of the quotients that presents all rational radical, operation which, as dictated by mathematical discipline, can only be carried out when the rational radicals involved in the operation are similar to each other, that is, they have equal index and the same establishment.

## How to solve a sum of rational radicals

As to the appropriate way in which any operation which proposes to calculate the total of two or more rational radicals must be solved, Mathematics dictates that the following steps must then be followed:

• If the sum is raised between rational radicals, it must be verified that they are similar, otherwise the operation cannot be continued.
• If they are then similar radicals, that is to say they have equal indices and as they are rooted in the same fraction, the coefficients must be added, assuming a single radical. If the coefficient is not explicitly found, it will be assumed that the coefficient is equal to 1.
• Calculated the total of the coefficients, the amount accompanied by the common or similar radical between the two additions is expressed.

The form indicated by the Mathematics to solve this operation may be expressed as follows:

## Examples of the sum of rational radicals

However, the most efficient way to study the correct way in which any sum of rational radicals should be resolved may be through the exposure of some examples, in which it may be seen in a practical way how each of the steps indicated by the mathematical theory. Here are some of them:

## Example 1

Solve the following sum of rational radicals:

Once the operation has been raised, the radicals of each factor should then be reviewed, in order to verify that they fully match both their indices and their establishments. Having done this, the values of the coefficients present in each factor will be added together, assuming a single radical:

## Example 2

Resolve the following operation:

At the time of beginning to resolve this operation, attention will be paid to the radicals, in order to determine whether they are similar. Verified that the radicals agree in both their indices and values, then we proceed to the sum of coefficients. However, one of the factors does not have an explicit coefficient. In this case it is assumed that the coefficient is equal to the unit:

## Example 3

Solve the following sum of rational radicals:

In this case, when checking the radicals, you will find that one of the factors or additions does not have a radical that is equal to the other two factors involved, which do have similar radicals. Consequently, the sum will be made among those who are similar. Similarly, of the two additions that do have similar radicals, one of them does not have an explicit coefficient, so it will be considered equal to the unit:

However, at this point the addition operation cannot be continued, since the factors obtained do not have similar radicals.

## Other examples

The following may also be taken as examples of the sum of rational radicals:

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