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Roots of Real Numbers

Roots of Real Numbers. An n th root ( ) of b is a solution of the equation. n is odd. n is even. If b>0, two real roots. Principal root is positive. If b<0, no real roots. If b>0, or b<0, there is exactly one real root. Roots of Real Numbers.

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Roots of Real Numbers

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  1. Roots of Real Numbers • An nth root ( ) of b is a solution of the equation . n is odd n is even If b>0, two real roots. Principal root is positive. If b<0, no real roots. If b>0, or b<0, there is exactly one real root.

  2. Roots of Real Numbers • Simplify the following roots:

  3. Roots of Real Numbers • What is the difference betweenthe following expressions?

  4. Roots of Real Numbers • What is the difference betweenthe following expressions?

  5. Roots of Real Numbers • Simplify the following:

  6. Learning Log Summary LT 1 – I can identify the roots of real numbers. The nth root is… If a negative number is in an odd/even root…

  7. Closure Homework (record on Learning Log): LT 1: pg. 262 ~ 1-13 (Odd) pg. 263 ~ Mixed Review 1-5

  8. Simplifying Radicals • Consider: and • Complete the following property of radicals:

  9. Simplifying Radicals • Consider: and • Complete the following property of radicals:

  10. CAUTION!!!! • The properties we just discovered DO NOT apply to addition and subtraction.

  11. Simplifying Radicals • Simplify:

  12. Simplifying Radicals • Rationalizing the Denominator means to re-write a fraction with a radical in the denominator so that the only radical is in the numerator. • To accomplish this, multiply by some form of 1 so that the denominator can be simplified without a radical. Ex 1) Ex 2)

  13. Learning Log Summary LT 2 – I can simplify expressions involving radicals. To simplify a number without the given root… Rationalizing the denominator means…

  14. Closure Homework (record on Learning Log): LT 2: pg. 267 ~ 1-31 (O), 39-45 (O)

  15. CONNECT 4 • Place any of the items from the answer bank into any space of your Connect 4 board without repeating. • You will not use all of the answers! • Solve each problem, and if the answer is on the board, place an X in the space. • First three people to Connect 4 win!

  16. Connect 4 Simplify:

  17. Connect 4 Simplify:

  18. Connect 4 Simplify:

  19. Connect 4 Simplify:

  20. Connect 4 Simplify:

  21. Connect 4 Simplify:

  22. Connect 4 Simplify:

  23. Connect 4 Simplify:

  24. Connect 4 Simplify:

  25. Connect 4 Simplify:

  26. Connect 4 Simplify:

  27. Connect 4 Simplify:

  28. Connect 4 Simplify:

  29. Connect 4 Simplify:

  30. Connect 4 Simplify:

  31. Checkpoint #1

  32. Checkpoint #2

  33. Checkpoint #3

  34. Checkpoint #4

  35. Learning Log Summary LT 3 – I can simplify expressions involving the sum of radicals. In order to add or subtract radicals… Roots that can be added or subtracted…

  36. Closure Homework (record on Learning Log): LT 3: pg. 272 ~ 1-25 (O)

  37. Multiplying / Dividing Radical Expressions Simplify the following:

  38. Multiplying / Dividing Radical Expressions Simplify the following:

  39. Multiplying / Dividing Radical Expressions Simplify the following:

  40. Conjugates Notice that the value of is an integer. Expressions of the form and are called conjugates. Multiplying by a conjugate “eliminates” the radicals.

  41. Multiplying / Dividing Radical Expressions Simplify the following:

  42. Multiplying / Dividing Radical Expressions Simplify the following:

  43. Learning Log Summary LT 4 – I can simplify the product and quotients of binomials that contain radicals. When multiplying radicals… If the denominator of a fraction contains a radical expression…

  44. Closure Homework (record on Learning Log): LT 4: pg. 275 ~ 1-29 (O)

  45. Solving Radical Equations Any equation that contains a variable in the radicand is called a radical equation. For example: As a non-example:

  46. Solving Radical Equations REVIEW – What is an extraneous solution? For Example:

  47. Solving Radical Equations Solve:

  48. Solving Radical Equations Solve:

  49. Learning Log Summary LT 5 – I can solve equations involving radicals. To solve a radical equation… LT6– I can identify extraneous solutions to radical equations, using appropriate justifications. An extraneous solution is…

  50. Closure Homework (record on Learning Log): LT 5/6: pg. 280 ~ 1-19 (O) pg. 282 ~ 1-12 (all) QUIZ on MONDAY on LT 1-6

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