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In this section, we will… Simplify Square Roots Simplify Higher-Order Roots

Chapter 8 Sections 3+4: Simplifying and Adding/Subtracting Radical Expressions. In this section, we will… Simplify Square Roots Simplify Higher-Order Roots Add and Subtract Radical Expressions.

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In this section, we will… Simplify Square Roots Simplify Higher-Order Roots

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  1. Chapter 8 Sections 3+4: Simplifying and Adding/Subtracting Radical Expressions • In this section, we will… • Simplify Square Roots • Simplify Higher-Order Roots • Add and Subtract Radical Expressions

  2. Properties of Radicals: Let a and b represent real numbers. Assuming that all radicals are defined: Simplifying Radicals: A radical is in simplest form when: • No square roots appear in the denominator of a fraction • The radicand cannot have any factors that are perfect squares • (perfect squares: 4, 9, 16, 25, 36, 49, 64…) Examples: Simplify each square root.

  3. Examples: Simplify each square root.

  4. Properties of Radicals: Let and denote positive integers and let a and b represent real numbers. Assuming that all radicals are defined: Simplifying Radicals: A radical is in simplest form when: • No radicals appear in the denominator of a fraction • The radicand cannot have any factors that are perfect roots (given the index) Examples: Simplify each expression.

  5. Adding and Subtracting Radical Expressions: • simplify each radical expression • combine all like-radicals (combine the coefficients and keep the common radical) Examples: Simplify each expression. Assume that all variables are positive.

  6. Examples: Simplify each expression. Assume that all variables are positive.

  7. Example: Find the total length of the patient’s arm in the illustration.

  8. Independent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved each problem; rework all problems that are incorrect. Read pp. 657-665 and 668-672 Homework: pp. 665-668 #1, 2, 3, 20, 21-31 odds,53, 55, 59-67 odds, 73, 75, 77, 83, 87 pp. 672-674 #1, 2, 17, 19, 21, 25-37 odds, 49, 53, 55, 61, 73, 89, 93, 94, 95-101 odds

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