Transcription of 9.2 Simplifying Radical Expressions
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9.2 Simplifying Radical Expressions
2001 McGraw-Hill Companies707 Simplifying Radical Expressions involving numeric Expressions involving algebraic radicalsIn Section , we introduced the Radical notation. For most applications, we will want tomake sure that all Radical Expressions are in simplest accomplish this, the follow-ing three conditions must be expression involving square roots is in simplest are no perfect-square factors in a fraction appears inside a Radical appears in the and Properties:Square Root Expressions inSimplest FormFor instance, considering condition 1,is in simplest form because 17 has noperfect-square factorswhereasis notin simplest formbecause it does contain a perfect-square perfect squareTo simplify Radical Expressions , we ll need to develop two important properties. First, lookat the following Expressions :Because this tells us that the following general rule for radicals 9 14 19,14 19 2 3 614 9 136 6112 14 3112117 For any positive real numbers aand b,In words, the square root of a product is the product of the square 1a 1bRules and Properties:Property 1 of Radicals708 CHAPTER9 EXPONENTS ANDRADICALS 2001 McGraw-Hill CompaniesSimplifying Radical ExpressionsSimplify each expression.
(b) Perfect squares (c) Perfect squares 3a212a 29a4 12a 218a5 29 a4 2a 2b1b 24b2 1b 24b3 24 b2 b x1x 2x2 1x 2x3 2x2 x The process is the same if variables are involved in a radical expression. In our remaining work with radicals, we will assume that all variables represent positive real numbers. Example 2 Simplify. (a) (b) (c) 29x3 227m3 250b5 ...
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