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Simplifying Radical Expressions

Simplifying Radical Expressions. Chapter 10 Section 1 Kalie Stallard. Radical Expression: an expression that contains a square root. Ex: Radicand: The expression under the square root sign. Expression is in Simplest Form when the radicand contains no perfect square factors other than 1.

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Simplifying Radical Expressions

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  1. Simplifying Radical Expressions Chapter 10 Section 1 KalieStallard

  2. Radical Expression: an expression that contains a square root. Ex: • Radicand: The expression under the square root sign. • Expression is in Simplest Form when the radicand contains no perfect square factors other than 1. • Is in simplest form? • Is 3 in simplest form?

  3. Product Property of Square Roots • The square root of the product ab is equal to the product of each square root. aand b both have to be ≥ 0 Example:

  4. Product Property of Square RootsSimplify the Following 3

  5. Product Property of Square RootsSimplify the Following • 3

  6. Simplify a Square Root with Variables • When finding the square root of an expression containing variables, be sure that the result is not negative. • = │x│ Let’s look at x=-2

  7. Quotient Property of Square Roots • The square root of is equal to each square root a and b. a and b both have to be ≥ 0 Example:

  8. Quotient Property of Square Roots

  9. Rationalizing the Denominator of a radical expression is a method used to eliminate radicals from a denominator. • Multiply by

  10. Rationalizing the Denominator • Multiply by

  11. Concept Summary • A radical expression is in simplest form when the following three conditions have been met. • No radicands have perfect square factors other than 1. • No radicands contain fractions • No radicals appear in the denominator of a fraction.

  12. Homework Page 531: #1-7, 17-31, 41-44

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