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Operations with Radicals Lesson 13.3 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 Like Radicals… Two radical expressions are like radicals if they have the same radicand. For instance, √2 and 3√2 are like radicals. To add or subtract like radicals, add or subtract their coefficients. √2 + 3√2 = (1 + 3)√2 = 4√2 √2 - 3√2 = (1 – 3)√2 = -2√2 Practice… 1. 2√3 + √2 - 4√3 1. 2. -2√3 + √2 Add like radicals. 3√2 - √8 1. 2. 3. 3√2 - √4 ∙ √2 3√2 - 2√2 √2 Product Property Subtract like radicals. Multiplying Radicals 3√2(√2 + 4√6) = (3√2)(√2) + (3√2)(4√6) Distributive Property = 3(√2 ∙ √2) + (3∙4)(√2∙ √6) Regroup = 3√4 + 12√12 Product Property = 3√4 + 12√4∙3 Perfect square factor = 3(2) + 12(2)√3 Simplify = 6 + 24√3 Simplest form Practice: simplify the radical expressions. 1. 4√3 - 5√3 -√3 2. -6√12 + √75 -6√4∙3 + √25∙3 -12√3 + 5√3 -7√3 Multiply and Simplify 1. 2√3(√2 + 5√6) 2√6 + 10√18 2√6 + 10√9∙2 2√6 + 30√2 2. 3√8(√3 – 5) 3√24 - 15√8 3√(4•6) - 15√(4•2) (3•2)√6 - 15•2√2 6√6 - 30√2