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Pre-Calculus 11 Section 2.2: Simplifying Radical Expressions Date: _____________________ Page 1 of 3 Review from Math 10: Parts of a radical Recall: Connection between Radical and Fractional exponent Note: the radical symbol only represents the _____________ square root, so 25 ______ ______ 72 and 3 128 are called ______________ radicals (everything underneath the symbol) whereas 6 2 and 43 2 are called _______________ radicals (a product of a monomial and a radical. Entire Radical: No coefficient (except negative 1 or 1) Mixed Radical: When possible, reduce entire radical to mixed radical with the smallest possible radicand. Also, rationalize the denominator so that the radicand is not a fraction. Pre-Calculus 11 Section 2.2: Simplifying Radical Expressions Date: _____________________ Page 2 of 3 Example 1: Convert entire radicals to mixed radicals… (see if you can do it two ways) 3 54x10 a) 150 b) Method 1: Prime factorization Method 1: Prime factorization Method 2: Greatest-Perfect Square Factor Method 2: Greatest-Perfect Cube Factor c) 72a 5b 4 c11 (use whichever method you like) NOTE: Examples b and c have variables in the radicand….do we need to be concerned by that? _______!!!. If a radical represents a real number and has an ________ index, then the ______________ must be _________________. Note: A radical is in SIMPLEST form when the radicand does not contain a fraction or any factor which may be removed. Example 2: Put the following numbers in order from least to greatest (no calculator use here!) 1 14 511 2 205 10 2 Solution: Write as entire radical. Pre-Calculus 11 Section 2.2: Simplifying Radical Expressions Date: _____________________ Page 3 of 3 Example 3: Convert mixed radicals to entire radicals. Now also identify the values of the variable for which the radical represents a real number for parts c and d! b) 10 3 2 d) 4a 2 b 3 2ab a) 5 3 c) x 5 2 x Home Learning: 2.2 page 100, #3,4,5b,6b,7a,8c,9(choose 1), 10 (choose 1), 11, (choose 1), 16a, do the study notes. Go over Checkpoint 1 on page 107, Higher Level: 12, 14, 16b