Examples of how to solve the rational root product

Perhaps best, prior to approaching some cases that may serve as an example of the correct way in which any procedure to find the Product of Rational Radicals must be resolved is to revise the very definition of this operation, in order to understand each of these exercises in their just mathematical context.

In this way, one can begin by remembering that Mathematics has explained rational radicals as any expression or operation where there is a radical who has as a settled a fraction, and that will be resolved to the extent that the fraction is determined that raised to the index offered by the operation, results in the expression of serving as settling, so then you could say that rational radicals are a reverse operation to the rational base power.

For their part, as regards the Product of rational radicals, the various sources have pointed out that this operation can be understood as the procedure by which a rational radical is added in itself, as many times as a second element points out, also composed of a rational radical. However, mathematical discipline indicates that for this operation to be possible, the factors involved must have matching radicals in their indices.

Steps to find the product of rational radicals

Mathematics has also indicated that each of the following steps must then be completed when solving such an operation:

1. Given a product operation of rational radicals, the first thing to do is to review the indices of the radicals involved. If it is of different indexes, the multiplication cannot be continued. Conversely, if these radicals agree on their indexes, the operation continues.
2. In this way, the product of the coefficients as well as that of the establishments must be found. In the event that a rational radical does not have an explicitly expressed coefficient, it will be assumed that the coefficient is equal to the unit. As for the product of the radicals, the coefficients and fractions that serve to each one are multiplied, and the index in which they matched is assumed as an index.

This operation can be expressed in mathematical terms as follows:

However, the most successful way of studying the product operation of rational radicals may be through the exposure of some examples, which allow us to see in practice how each of the steps, indicated by the Mathematics, are fulfilled. Here are some of them:

Example 1

Resolve the following operation:

When you start solving the proposed operation, the first thing to do is to review the indices of each of the radicals. In this case both are square roots, so the operation continues, multiplying both coefficients and filings:

Example 2

Find the following product of rational radicals:

To start the operation, it is then reviewed that both radicals match their indexes. In this case, the two radicals present as index 3, because they are cubic roots. It then multiplies rational coefficients and establishments. However, there is the particularity that one of the coefficients is not explicitly expressed, so it is then assumed to be equal to 1:

Example 3

Resolve the following operation:

It may also be that the coefficients are also made up of rational number, in which case there will be no problem, and the operation will be solved by multiplying the coefficients and the establishments, provided that the only requirement is met, which these match their indices:

Example 4

Calculate the following rational radical product:

It may also happen that once the radicals match their indices has been found, it is also the case that the coefficients are composed of one by an integer, and the other by a rational number. In this case, it should be remembered that the whole number can be expressed as fraction, assuming the unit as denominator, which will allow it to multiply with the other coefficient:

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Examples of how to solve the rational root product
Source: Education
October 17, 2019