1. Operations with Radicals Lesson 13.3

2. 43210 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 The student will be able to use properties of rational and irrational numbers to write and simplify expressi ons based on contextual situations. -identify parts of an expression as related to the context and to each part With help from the teacher, the student has partial success with real number expressions. Even with help, the student has no success with real number expressions. 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.

3. 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

4. Practice… 1. 2√3 + √2 - 4√3 1. -2√3 + √2 Add like radicals. 2. 3√2 - √8 1. 3√2 - √4 ∙ √2 Product Property 2. 3√2 - 2√2 Subtract like radicals. 3. √2

5. 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

6. Practice: simplify the radical expressions. 1. 4√3 - 5√3 2. -6√12 + √75 -√3 -6√4∙3 + √25∙3 -12√3 + 5√3 -7√3

7. Multiply and Simplify 1. 2√3(√2 + 5√6) 2. 3√8(√3 – 5) 2√6 + 10√18 2√6 + 10√9∙2 2√6 + 30√2 3√24 - 15√8 3√(46) - 15√(42) (32)√6 - 152√2 6√6 - 30√2