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.
A perfect square (b) A perfect square (c) A perfect square (d) A perfect square Be Careful! Even though is not the same as Let a 4 and b 9, and substitute. Because we see that the expressions and are not in general the same. 13 5,1 a b 1a 1b 14 19 2 3 5 1a b 14 9 113 1a b 1a 1b 1a b 1a 1b 5 19 12 5 3 12 1512 5118 519 2 612 136 12 172 136 2 315 ...
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