Simplifying Radical Expressions Guide
Learn how to simplify radical expressions with step-by-step examples and techniques such as finding prime factorization and using perfect square factors. Improve your understanding of radicals in mathematics.
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Presentation Transcript
10.2 a Simplifying Radicals Who uses this? Forest, conservation and logging workers Economists Actuary Statistician Engineer Insurance underwriters
Vocabulary a radical symbol radicand the number underneath the radical radical expression An expression that has radicals in it
Ways to Simplify A Radical Expression Option 1 Find the prime factorization of the radicand Every 2 equal factors under the radical sign is equivalent to one of those factors outside of the radical
Examples 75 = 3 5 5 = 5 3 2 5 3 = = = 2 2 3 5 5 300 10 3 = = 2 2 3 5 2 15 60 = = = 8 4 2 2 4 2 4 2 2
Ways to Simplify A Radical Expression Option 2 Express the radicand using perfect square factors Use the Product Property of Square Roots to simplify
Examples = = 75 5 3 25 3 = 25 3 = = = 300 100 3 10 3 100 3 = = 2 15 = 4 15 4 15 60 = = 4 2 8 = = 4 2 2 4 4 4 2 2
Examples = = 20 2 5 = 2 10 4 5 = = = 9 5 15 3 45 3 5 = = = 18 2 3 36 2 3 72 12 3 6 ( ) 42 35 = 14 315 = 14 9 35 = 7 15 2 21
Examples 3x 2 4 x y x x x x x y y y y 1 x 2 x xy 5 9 x y 4 6 16x y y x x x x x y y y y y y y y y 2 3 x 4 4 2 y y x x
Examples 3 3 5 15 x x 9 48x 2 2 2 2 3 x x x x x x x x 4 3 75x 3 5 3 5 x x x x 4 4 3 x x 2 15 x 3
Examples 2 5 3 12 2 20 x x 7 6 240x 6 2 2 2 2 5 3 x x x x x x 3 15 24 x x
