2. Real World Problems Complex Number i Mystery ?? Rational vs. Irrational Rational Exponents 50 40 30 20 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50

3. What do rational exponents represent? Answer

4. Roots Radicals Is “square roots” a correct answer?

5. Rewrite the following expression using rational exponents, then simplify it: Answer

7. Simplify the following expression using your knowledge of rational exponents. (-3y 1/3 )(-2y 1/2 ) Answer

8. 6y 5/6

9. True or False?? Answer

10. True

11. True or False?? Answer

12. True

13. Rational + Rational=?? Irrational +Irrational =?? Answer

14. Rational Irrational and rational example: √2 - √2 = 0

15. Rational +Irrational=?? Answer

16. Irrational Is this always the case?

17. Are Irrational numbers Real? That is can we place them on a number line? Give an example. Answer

18. Yes, irrational numbers are real; we can place them on a number line. (Recall the ruler activity).

19. Draw a right triangle with an irrational hypotenuse length. Answer

20. (Compliments of Google.com)

21. Define rational number. Define irrational number, and give an example. Answer

22. Rational number: def: A number that can be written in the form a/b, where a, b are integers and b≠ 0 Irrational number: def: a number that cannot be written in the form a/b, where a, b are integers and b≠ 0. An irrational number has a non-repeating decimal. Example: pi, sqrt 2, sqrt 15

23. Simplify the expression 8 -4/3 Answer

24. 1/16

25. Rewrite the following in radical form: a(b 4 +1) -1/2 Answer

27. Which letters represent irrational numbers and why? a.3.1415926454….. b..66666666…… c..7317311731117311111 … d..123123123123…… Answer

28. a. and c. represent irrational numbers. We know this because the decimals are non-repeating.

29. Simplify i^49 Answer

30. i

31. Simplify (7+6i)(3-2i)(3i) Answer

32. -12+99i

33. Simplify i^14 Answer

34. i^2

35. Simplify (2+3i)+(4-i) Answer

36. 6+2i

37. Simplify (7+4i)-(8-3i) Answer

38. 1+7i

39. Simplify Define a complex number Answer

40. Any number a+bi where a and b are real numbers.

41. Simplify (5+7i)(6-7i) Answer

42. 79+7i

43. Cindy has a piece of ribbon that is 4/5 of a foot long. How long would each piece be if she cut the ribbon in half? Answer

44. Each half of the ribbon would be 4.8 inches long

45. Tool box problem: Longest Screwdriver A toolbox has length L, width W, and height H. The length D of the longest screwdriver that will fit inside the box is given by: D = (L 2 + W 2 + H 2 ) 1/2 Find the length of the longest screwdriver that will fit in a 4 in. by 6 in. by 12 in. box. Answer

46. 14 inches

47. Find the error (2+4i)(3-6i) =6-12i+12i-24i =6-24i Answer

48. (2+4i)(3-6i) =6-12i+12i-24i^2 =6-24(-1) =30

49. Where do irrational numbers originate from? What happened to the man who promoted irrational numbers? Answer

50. Irrational numbers originate from mathematicians who were working with the Pythagorean Theorem. They discovered that a right triangle with legs of unit length 1 would have a hypotenuse of the square root of two. The man who promoted irrational numbers, Greek mathematician Hippasus, was taken to sea and never returned!

51. Jared wants to cut a rectangle of paper diagonally. He wants the diagonal to be square root 5 inches in length. What lengths, in inches, do each of the sides of the rectangle need to be to give Jared the diagonal that he wants? Answer

52. The sides of the rectangle need to be the square root of 4 inches and 1 inch.