## PinkSapphire one year ago Simplify by rationalizing the denominator.

1. blackstreet23

Pardon me but simplify which fraction?

2. PinkSapphire

$\frac{ \sqrt{11} }{ 5\sqrt{132} }$

3. PinkSapphire

Sorry, my internet is really slow today.

4. PinkSapphire

@blackstreet23

5. PinkSapphire

For my answer, am I supposed to get rid of the square root in the denominator?

6. blackstreet23

ohh ok well for rationalyze you just need to multiply the fraction by the number on the denominator as a fraction so it equals to one

7. blackstreet23

example $1/\sqrt{2}$

8. PinkSapphire

I think I did that, but I'm not sure that I understood you completely.

9. blackstreet23

hold on

10. blackstreet23

so yeah to rationalize that you would have to multiply the previous fraction by the number in the denominator as a fraction I mean $\sqrt{2}/\sqrt{2}$

11. blackstreet23

that is the same as multiplying by one

12. blackstreet23

so you are not really changing the fraction itself, just how it looks

13. blackstreet23

is like if you get a hair cut, you may change how you look but you are still the same person.

14. blackstreet23

does that help a little?

15. blackstreet23

what have you done so far?

16. PinkSapphire

Okay, I think I did that.

17. blackstreet23

$\frac{1 }{ \sqrt{2} } * \frac{ \sqrt{2} }{ \sqrt{2} }$

18. blackstreet23

ohh ok.

19. blackstreet23

is that the answer on the back of the book?

20. PinkSapphire

What book?

21. blackstreet23

you did not take this question from a math book? ohh is ok then. I was just wondering so i made sure you had 100% the right answer

22. PinkSapphire

Well, it is from my math book but we don't have the answers in the book.

23. PinkSapphire

Right now my laptop is really slow so I'm using my phone but I don't know how to type my answer in because of the radical signs.

24. blackstreet23

ohh just go to equation on the bottom of the text rectangle it has the sigma sign$\sum_{}^{}$

25. blackstreet23

and i just asked because in all my math books we always have the answers so we know we are doing it right haha

26. PinkSapphire

On the phone it doesn't have that.

27. blackstreet23

Could you use your phone as a hotspot so you use the phone's internet on your laptop?

28. blackstreet23

anyway, just write what you have using root(#)

29. blackstreet23

i will get it

30. PinkSapphire

I think I'll try it on the Safari app instead of the OpenStudy app.

31. PinkSapphire

I think I'll try it on the Safari app instead of the OpenStudy app.

32. PinkSapphire

No, it doesn't have it on there either.

33. PinkSapphire

It's working! Okay, this is the answer that I got:$\frac{ \sqrt{11} }{ 10\sqrt{33} }$

34. blackstreet23

just write it how i told you. I will try to get it :D

35. blackstreet23

ohh ok

36. PinkSapphire

Did you get a different answer?

37. blackstreet23

that is perfect so far

38. blackstreet23

but still incomplete

39. blackstreet23

you can factor it a little bit more

40. blackstreet23

what are the factors of 33?

41. PinkSapphire

3 and 11?

42. blackstreet23

yes. so what could cancel?

43. PinkSapphire

$\sqrt{11}$

44. PinkSapphire

Right?

45. blackstreet23

yes

46. blackstreet23

so what are you left with?

47. PinkSapphire

$10\sqrt{3}$

48. PinkSapphire

Right?

49. blackstreet23

actually $1/10\sqrt{3}$

50. blackstreet23

but yes

51. blackstreet23

and the last step is to do what i told you previously

52. PinkSapphire

Oh yeah, my mistake.

53. blackstreet23

make a fraction with the rational in the denominator of the first fraction. That fraction must equal to 1

54. PinkSapphire

I don't understand.

55. blackstreet23

which is the rational on the denominator of the fraction you have now?

56. PinkSapphire

$\sqrt{3}$

57. blackstreet23

so take that rational and make a fraction that equals 1

58. blackstreet23

do you know how to do it?

59. blackstreet23

$\frac{ 5 }{ 5 }$

60. blackstreet23

rings a bell?

61. PinkSapphire

How did you do that?

62. blackstreet23

ohh no i was just showing you that any number over itself equals one

63. blackstreet23

K/K = 1

64. blackstreet23

k = constant

65. blackstreet23

or any polynomial

66. blackstreet23

over itself is equal to 1

67. blackstreet23

so lets say

68. blackstreet23

$\frac{ \sqrt{3} }{ \sqrt{3} } = 1$

69. PinkSapphire

Okay...

70. blackstreet23

and that is what you would have to multiply so you are not actually altering the fraction, just changing how it looks :P

71. blackstreet23

you get it?

72. PinkSapphire

Not really. I'm sorry, but can you show it to me with numbers?

73. blackstreet23

you mean the concept that every number over itself equal 1 or how to finish your problem?

74. PinkSapphire

How to finish my problem.

75. blackstreet23

just multiply $\frac{ \sqrt{3} }{ \sqrt{3} } * (previous fraction)$

76. blackstreet23

that is what i meant

77. mathstudent55

|dw:1441502937030:dw|

78. blackstreet23

$\frac{ \sqrt{3} }{\sqrt{3} } * \frac{ \sqrt{1} }{ 10\sqrt{3} }$

79. blackstreet23

yes exactly

80. mathstudent55

$$\dfrac{ \sqrt 3 }{\sqrt 3 } \times \dfrac{ \color{red}{1} }{ 10\sqrt 3 }$$

81. blackstreet23

yes you are right @mathstudent55 even though is the same thing haha i mean 1 and root (1), but yeah for clarity just 1 is better

82. mathstudent55

You can also do it this way. |dw:1441503409900:dw|

83. blackstreet23

yes that is the answer $\frac{ \sqrt{3} }{ 30 }$

84. PinkSapphire

Okay, I get it. Thanks @blackstreet23 and @mathstudent55

85. blackstreet23

No problem, here to help :) good luck !

86. mathstudent55

You're welcome.

87. PinkSapphire

Thanks for taking the time to help me! :)