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Warm-Up: November 29, 2011

Warm-Up: November 29, 2011. Simplify the following:. Radical Expressions. Section 5-6. Product Property of Radicals. If n is an even natural number, and a and b are positive real numbers If n is an odd natural number, and a and b are real numbers. Simplifying Square Roots.

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Warm-Up: November 29, 2011

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  1. Warm-Up: November 29, 2011 • Simplify the following:

  2. Radical Expressions Section 5-6

  3. Product Property of Radicals • If n is an even natural number, and a and b are positive real numbers • If n is an odd natural number, and a and b are real numbers

  4. Simplifying Square Roots • Factor the radicand into as many perfect squares as possible. • Can use a factor tree for the coefficient, and find pairs of the same factor • Use the product property to isolate the perfect squares. • Simplify each radical.

  5. Example 1 • Simplify

  6. You-Try #1 • Simplify

  7. Quotient Property of Radicals • If n is an even natural number, and a and b are positive real numbers • If n is an odd natural number, and a and b are real numbers, and b≠0

  8. Simplifying Radical Expressions All of the following must be true to be in simplified form: • The index, n, must be as small as possible. • The radicand contains no factors (other than 1) that are nth powers of an integer or polynomial. • The radicand contains no fractions. • No radicals appear in the denominator. • The process of eliminating radicals from a denominator is called rationalizing the denominator.

  9. Example 2 - Simplify each expression

  10. You-Try #2 – Simplify each Expression

  11. Assignment • Page 254 #15-29 odd

  12. Warm-Up: November 30, 2011 - Simplify

  13. Homework Questions?

  14. Example 3 – Multiplying Radicals • Simplify

  15. You-Try #3 – Multiplying Radicals • Simplify

  16. Adding and Subtracting Radicals • Only like terms can be combined • Index of the radicals must be the same • Radicands must be the same • Simplify radicals before attempting to combine • Like terms are combined the same way that “x” terms are combined

  17. Example 4 • Simplify

  18. You-Try #4 • Simplify

  19. Example 5 – Multiplying Radical Expressions • Simplify each expression

  20. Warm-Up: December 1/2, 2011Simplify Each Expression

  21. Homework Questions?

  22. You-Try #5 – Multiplying Radical Expressions • Simplify each expression

  23. Conjugates • Binomials that differ by one sign (+ vs -) are called conjugates.

  24. Example 6 – Simplify Using Conjugate

  25. You-Try #6 – Simplify Using Conjugate

  26. Assignment • Page 254 #31-45 odd

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