![]() Go to the next section to see examples with cube roots. Created by Sal Khan and Monterey Institute for Technology and Education. In this example, we simplify (60xy)/ (48x). Next, clean up the problem to get the final answer. Simplifying radical expressions: two variables Google Classroom About Transcript A worked example of simplifying elaborate expressions that contain radicals with two variables. Definition 8.3. The corresponding of Product Property of Roots says that nab na nb. The properties we will use to simplify radical expressions are similar to the properties of exponents. Note that a perfect square number has a rational square root. To simplify radical expressions, we will also use some properties of roots. Place a factor on the outside of the radical for each group. In this video, we are going to simplify radical expressions. The index is 2, so we will group in pairs. Now, we will write the prime factors under a radical. This is a factor tree for the radicand 72. Anything ungrouped will remain under the radical, like so. This means we group the factors in groups of two, like so.įor each group, a factor comes out. So, we will write these in place of the 12 under the radical. However, 4 is not prime (called composite) and it can be factored as follows. 3 is prime because it has no other smaller factors other than 1. This allows us to focus on simplifying radicals without the technical issues associated with the principal (n)th root. We typically assume that all variable expressions within the radical are nonnegative. Our only other option is to simplify the radical using the steps outlined within our graphic organizer in the last section, Steps for Simplifying Radical Expressions. A radical expression is simplified if its radicand does not contain any factors that can be written as perfect powers of the index. try this factorization: Simplify:. If we were to use a calculator to find the solution, it would provide us with a decimal solution somewhere between 3 and 4. 6.2 - Simplifying Radical Expressions using Multiplication and Division. This problem does not have a perfect answer. The best way to learn how to simplify an expression is to examine an example. ![]()
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