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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 .

radicals. NOTE Apply Property 2. Apply Property 2. NOTE Factor 8x as 4x2 2. NOTE Apply Property 1 in the numerator. Simplify. (a) (b) (c) B 12x2 A 49 7 A 9 25 16 CHECK YOURSELF 3 For any positive real numbers a and b, In words, the square root of a quotient is the quotient of the square roots. A a b 1a 1b Rules and Properties: Property 2 of ...

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