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Simplifying Radicals Lesson 13.2 Learning Goal 1 (HS.N-RN.B3 and HS.A-SSE.A.1): The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions based on contextual situations. 4 3 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions on contextual situations. - justify the sums and products of rational and irrational numbers -interpret expressions within the context of a problem 2 1 0 The student will With help Even with be able to use from the help, the properties of teacher, the student has rational and student has no success irrational partial with real numbers to write success with number and real number expressions. simplify expressi expressions. ons based on contextual situations. -identify parts of an expression as related to the context and to each part An expression with radicals is in simplest form if the following are true: 1. No radicands (expressions under radical signs) have perfect square factors other than 1. 82 2 2. No radicands contain fractions. 7 7 9 3 3. No radicals appear in the denominator of a fraction. 1 1 4 2 Product Property • The square root of a product equals the product of the square root of the factors. ab a b • For example: 50 25 2 5 2 Quotient Property • The square root of a quotient equals the quotient of the square root of the numerator and denominator. a a b b • For example: 3 4 3 4 3 2 If the radical in the denominator is not the square root of a perfect square, then a different strategy is required. Simplify 1 . To simplify this expression, multiply the numerator and denominator by √2. 2 1 1 2 2 2 2 1 2 2 2 2 4 2 2 Practice… 1. 75 25 3 5 3 2. 180 36 5 6 5 3. 49 121 49 121 4. 3 12 1 5. . 8 = 7 11 3 ∙ √12 = 3 ∙ 2√3 √12 √12 12 = √1 ∙ √8 √8 √8 = √8 8 = √3 2 = 2√2 = √2 2∙4 4 Find the area of a rectangle… • Find the area of a rectangle whose width is √2 inches and whose length is √30 inches. Give the result in exact form (simplified) and in decimal form. Area = Length ∙ Width √30 in. √2 in. = √30 ∙ √2 = √60 = √4 ∙ √15 = 2√15 about 7.746 square inches.