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11.2 Simplifying Radical Expressions

11.2 Simplifying Radical Expressions. Product Properties for Radicals. For any nonnegative real numbers x and y the property works in both of the following ways . a. b. Rules for Radical Expressions. Simplify the radicand first

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11.2 Simplifying Radical Expressions

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  1. 11.2Simplifying Radical Expressions

  2. Product Properties for Radicals • For any nonnegative real numbers x and y the property works in both of the following ways. a. b.

  3. Rules for Radical Expressions • Simplify the radicand first • When odd powers occur, express the power as the product of the largest even power and your exponential base. • Simplify the perfect squares.

  4. #5 Simplify

  5. #7 Simplify

  6. Using the Product Properties

  7. #8 Simplify

  8. Can you take the square root of a negative number? NO Because a negative number squared is positive

  9. #9 Simplify • All even powers are perfect squares.

  10. #10 Simplify

  11. #11 Simplify

  12. #12 Simplify

  13. #13 Simplify • Express odd powers as the product of the largest even power and your exponential base.

  14. #14 Simplify

  15. #15 Simplify

  16. The Quotient Rule for Radicals

  17. A Radical Expression is Simplified When: • Each factor in the radicand is to a power less than the index of the radical • The radicand contains no fractions or negative numbers • No radicals appear in the denominator of a fraction

  18. Leave no fractions or negative numbers in the radicand

  19. No radicals remain in the denominator of a fraction

  20. Adding & Subtracting Like Radicals • Each term must have a radical with identical index and radicand • Law of distribution allows combining or factoring • Like radicals: • Unlike radicals (cannot combine)

  21. Simplify before Trying to Combine

  22. Multiply Radicals with Distributive Prop.

  23. Classwork/homework

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