1. Simplifying Radicals Lesson 13.2

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. 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. 2.No radicands contain fractions. 3.No radicals appear in the denominator of a fraction.

4. Product Property The square root of a product equals the product of the square root of the factors. For example:

5. Quotient Property The square root of a quotient equals the quotient of the square root of the numerator and denominator. For example:

6. 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.

7. Practice… 5.. = 3 ∙ √12 √12 √12 = 3 ∙ 2√3 12 = √3 2 = √1 ∙ √8 √8 √8 = √8 8 = 2√2 = √2 2∙4 4

8. 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. √2 in. √30 in. Area = Length ∙ Width = √30 ∙ √2 = √60 = √4 ∙ √15 = 2√15 about 7.746 square inches.