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College Algebra K /DC Friday, 11 October 2013

College Algebra K /DC Friday, 11 October 2013. OBJECTIVE TSW simplify expressions with radicals. ASSIGNMENT DUE TUESDAY, 10/15/13 Sec. R.6: p. 59 (3-35 all) ASSIGNMENT CHANGE FOR TODAY Sec. R.7: pp. 70-71 (15-59 odd, 61-76 all) QUIZ on Tuesday, 15 October 2013

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College Algebra K /DC Friday, 11 October 2013

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  1. College Algebra K/DCFriday, 11 October 2013 • OBJECTIVETSW simplify expressions with radicals. • ASSIGNMENT DUE TUESDAY, 10/15/13 • Sec. R.6: p. 59 (3-35 all) • ASSIGNMENT CHANGE FOR TODAY • Sec. R.7: pp. 70-71 (15-59 odd, 61-76 all) • QUIZ on Tuesday, 15 October 2013 • Sec. R.6: No calculators, but you may use an exponents chart. You will do this next week!

  2. Radical Expressions R.7 Radical Notations ▪ Simplified Radicals

  3. Radical Definitions Notation for a1/n If a is a real number, n is a positive integer, and a1/n is a real number, then Notation for am/n If a is a real number, m is an integer, n is a positive integer, and is a real number, then

  4. Principle Square Root / Principle nth Root A principle square root (principle nth root)isALWAYSpositive!!!

  5. Radical Definitions Evaluating___ If n is an even positive integer, then If n is an odd positive integer, then Use absolute value only when necessary.

  6. Radical Definitions Product Rule Quotient Rule Power Rule If the indices are the same, multiply the radicands (numbers under the radical).

  7. CAUTION !!!!! You cannot distribute exponents over a sum!!!!!! ex: ex:

  8. Evaluating Roots • Write each root using exponents and evaluate. (a) (b) (c) is not a real number. (d)

  9. Evaluating Roots • Write each root using exponents and evaluate. (e) (f)

  10. Converting From Rational Exponents to Radicals • Write in radical form and simplify. (a) (b) (c) (d)

  11. College Algebra K/DCTuesday, 15 October 2013 Test has been moved to Monday, 10/21/13. • OBJECTIVETSW simplify expressions with radicals. • ASSIGNMENT DUE • Sec. R.6: p. 59 (3-35 all)  wire basket • Sec. R.6: p. 60 (47-70 all)  black tray • ASSIGNMENT CHANGE • Sec. R.7: pp. 70-71 (15-59 odd)  due tomorrow • Sec. R.7: p. 71 (61-76 all)  due tomorrow • Sec. R.7: p. 71 (85-93 all)  due test day • QUIZ: Sec. R.6 • Will be given at the beginning of class • 20 minutes max to work on it. • No calculators, but you may use an exponents chart.

  12. Using Absolute Value to Simplify Roots • Simplify each expression. (a) (b) (c) (d)

  13. Using Absolute Value to Simplify Roots • Simplify each expression. (e) (f) (g)

  14. Using the Rules for Radicals to Simplify Radical Expressions • Simplify each expression. (a) (b) (c)

  15. Using the Rules for Radicals to Simplify Radical Expressions • Simplify each expression. (d) (e) (f)

  16. Assignment: Sec. R.7: pp. 70-71 (15-59 odd)Due today, Wednesday, 16 October 2013 • Copy the problem, then simplify. • Copy the problem, then simplify.

  17. College Algebra K/DCWednesday, 16 October 2013 • OBJECTIVETSW simplify expressions with radicals. • ASSIGNMENT CHANGE • Sec. R.7: pp. 70-71 (15-59 odd)  wire basket • Sec. R.7: p. 71 (62-76 even)  due by end of period today • Sec. R.7: p. 71 (85-93 all)  due test day Test has been moved to Monday, 10/21/13.

  18. Radical Expressions R.7 Simplifying, Adding, Subtracting, and Multiplying Radicals

  19. Simplifying Radicals • Simplify each radical. (a) (b) (c)

  20. Adding and Subtracting Like Radicals • NOTE: When adding, subtracting, and multiplying, we will assume that all variables are positive. • Add or subtract as indicated. Subtract coefficients (a) Same radicand (b) Different radicands – simplify first

  21. Adding and Subtracting Like Radicals • Add or subtract as indicated and simplify. (c) already simplified (d)

  22. Simplifying Radicals by Writing Them With Rational Exponents • Simplify each radical. (a) (b) (c)

  23. Multiplying Radical Expressions • Find the product. Product of the sum and difference of two terms.

  24. Multiplying Radical Expressions Simplify • Find the product. FOIL

  25. Assignment: Sec. R.7: p. 71 (62-76 even)Due today, Wednesday, 16 October 2013 black tray • Copy the problem, then simplify.

  26. Rationalizing Denominators • Rationalize each denominator. (a) “What is the index of the denominator?” 2 (b) “What will make the denominator a perfect square?” 49

  27. Simplifying Radical Expressions with Fractions • Simplify the expression. Simplify radicand. Quotient rule Quotient rule Rationalize denominator.

  28. Simplifying Radical Expressions with Fractions • Simplify the expression. Simplify radicand. Quotient rule Multiply top and bottom by the conjugate of the denominator.

  29. Simplifying Radical Expressions with Fractions • Simplify the expression. Simplify radicand. Quotient rule

  30. Simplifying Radical Expressions with Fractions • Simplify the expression. Simplify radicand. Quotient rule

  31. Simplifying Radical Expressions with Fractions • Simplify the expression. Simplify radicand. Quotient rule

  32. Assignment: Sec. R.7: p. 71 (85-93 all)Due Monday, 21 October 2013 • Copy the problem, then rationalize the denominator.

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