Name: Block: Date: Pre-Calculus 11 Sec 5.1 Working with Radicals Objectives: • Converting between mixed radicals and entire radicals • Comparing and ordering radical expressions • Identifying restrictions on the variable within a radical sign • Simplifying radicals using addition and subtraction Rules of Divisibility: A number is divisible by 2- when the last digit is 0, 2,4,6,8 3- when the sum of all the digits is a # divisible by 3 5- when the last digit is 0 or 5 Write in prime factorization: 12, 28, 144 Perfect Square versus not a perfect square: 25 and 10 25 2 10 Like Radicals: (same radicand and index) When adding or subtracting radicals, only like radicals can be combined. Pairs of like radicals Pairs of unlike radicals 1 Restrictions on Variables: If a radical represents a real number and has an even index, the radicand must be non-negative. The radical 4 − x must be greater than or equal to zero. Mixed Radical Entire Radicals: Express each mixed radical in entire radical form: (don’t forget restrictions!) Ex.1) a) 7 2 d) 4 3 Entire Radicals Ex 2) a) b) a4 a e) j3 j 3 2 c) 5b 3b Mixed Radicals: (restrictions!!) 200 4 b) c9 c) 48y 5 Compare and Order Radicals: 1 4 (13) 2 , 8 3, 14, 202, 10 2 Order the radicals from least to greatest WITHOUT using a calculator!! You must convert them into entire radicals first. Ex. 3) Order the following radicals from least to greatest (no calculator!!) 5, 3 3, 2 6, 23 Add and Subtract Radicals: Ex. 4) Simplify radicals and combine like terms. a) d) 50 + 3 2 b) 4c − 4 9c , c ≥ 0 c) − 27 + 3 5 − 80 − 2 12 20 x − 3 45 x , x ≥ 0 Ex. 5) Consider the following designs shown for a skateboard ramp. What is the exact distance across the base?

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