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Simplifying Radicals This handout is a quick overview of simplifying radicals. We will revisit this information in Chapter 10 of this textbook. Product Rule of Radicals If a and b are positive real numbers, then ab a b = We know that 64 is a perfect square and 64 8 = . We can also simplify this using the property above. 64 16 4 16 4 4 2 8 = = = = i i When dealing with radicals, not always will the number under the radical be a perfect square. Thus, we need to discuss how to simplify them. Example: Simplify 75 Solution: 75 is not a perfect square, but we can factor 75 into 25 3 i . Notice that one of the factors is a perfect square. 75 25 3 25 3 5 3 = = = i We know we are done simplifying the radical when there are no more perfect squares under the radical. Example: Simplify 8 Solution : Factor 8 into 4 2 i 8 4 2 4 2 2 2 = = = i Example: Simplify 120 Solution : Factor 120 into 4 30 i 120 4 30 4 30 2 30 = = = i Example: Simplify 2 98 Solution : Factor 98 into 2 49 i 2 98 2 2 49 2 49 2 2 7 2 14 2 = = = = i Example: Simplify 5 50 - Solution : Factor 50 into 2 25 i 5 50 5 2 25 5 25 2 5 5 2 25 2 - = - = - = - = - i

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