1. Simplifying Radicals

2. Perfect Squares 64
225 1 81
256 4
100
289 9
121 16
324
144 25
400
169 36
196 49
625

3. How do you simplify variables in the radical?
Look at these examples and try to find the pattern…
What is the answer to ?
As a general rule, divide the exponent by two. The remainder stays in the radical.

4. Simplifying variable radicandsX² X

5. Simplify = = =
This is a piece of cake! = =

6. Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

7. Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

8. Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

9. Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

10. + To combine radicals: combine the coefficients of like radicals
Combining Radicals +
To combine radicals: combine the coefficients of like radicals

11. Simplify each expression

12. Simplify each expression

13. Simplify each expression: Simplify each radical first and then combine.

14. Simplify each expression: Simplify each radical first and then combine.

15. Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

16. Simplify each expression

17. Simplify each expression

18. WORKSHEET 3)

19. 5) 7)

20. 9)

21. 11)

22. 13)

23. 15)

24. 17)

27. Multiplying Radicals *
To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

28. Multiply and then simplify

30. WORKSHEET(MULT)

31. WORKSHEET(MULT)

32. WORKSHEET(MULT)

33. WORKSHEET(MULT)

34. WORKSHEET(MULT)

35. WORKSHEET(MULT)

36. Using distributive Property
a(b+c) = ab + ac
a(b-c) = ab - ac

37. USING THE DISTRIBUTIVE PROPERTY

38. USING THE DISTRIBUTIVE PROPERTY

39. USING THE DISTRIBUTIVE PROPERTY

40. USING THE DISTRIBUTIVE PROPERTY

41. USING THE DISTRIBUTIVE PROPERTY

42. USING THE DISTRIBUTIVE PROPERTY

43. USING THE DISTRIBUTIVE PROPERTY

44. USING THE DISTRIBUTIVE PROPERTY

45. Using the FOIL

46. Using the FOIL

48. Using the FOIL

49. Dividing Radicals
To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator

50. That was easy!

51. 42 cannot be simplified, so we are finished.
This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.
42 cannot be simplified, so we are finished.

52. This can be divided which leaves the radical in the denominator
This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

53. This cannot be divided which leaves the radical in the denominator
This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

54. This cannot be divided which leaves the radical in the denominator
This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

55. How do you simplify variables in the radical?
Look at these examples and try to find the pattern…
What is the answer to ?
As a general rule, divide the exponent by two. The remainder stays in the radical.

56. How do you simplify variables in the radical?
Look at these examples and try to find the pattern…
As a general rule, divide the exponent by two.

57. Simplify = = = = =

58. Simplify = = = = =

59. Simplify = = = =

60. = = ? = =