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). The variable could represent a positive or. 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. Now when working with square roots and variables we should be a bit careful. Place a factor on the outside of the radical for each group. 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. Use the product rule to rewrite the radical as the product of two radicals. Rewrite the radicand as a product of two factors, using that factor. Find the largest factor in the radicand that is a perfect power of the index. Anything ungrouped will remain under the radical, like so. Simplify a radical expression using the Product Property. 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. To simplify radical expressions, look for exponential terms within the. However, 4 is not prime (called composite) and it can be factored as follows. A radical expression is a mathematical way of representing the th root of a number. 3 is prime because it has no other smaller factors other than 1. 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. If we were to use a calculator to find the solution, it would provide us with a decimal solution somewhere between 3 and 4. Solution: Apply the product rule for radicals, and then simplify. Given real numbers nA and nB, nA nB nA B Example 5.4.1: Multiply: 312 36. This problem does not have a perfect answer. When multiplying radical expressions with the same index, we use the product rule for radicals. The best way to learn how to simplify an expression is to examine an example.
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