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Simplifying Radicals

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.

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Simplifying Radicals

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  1. Simplifying Radicals Lesson 13.2

  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.

  3. An expression with radicals is in simplest form if the following are true: • No radicands (expressions under radical signs) have perfect square factors other than 1. • No radicands contain fractions. • 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… • . = 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. Area = Length ∙ Width = √30 ∙ √2 = √60 = √4 ∙ √15 = 2√15 about 7.746 square inches. √2 in. √30 in.

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