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PinkSapphire

  • one year ago

Simplify by rationalizing the denominator.

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  1. blackstreet23
    • one year ago
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    Pardon me but simplify which fraction?

  2. PinkSapphire
    • one year ago
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    \[\frac{ \sqrt{11} }{ 5\sqrt{132} }\]

  3. PinkSapphire
    • one year ago
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    Sorry, my internet is really slow today.

  4. PinkSapphire
    • one year ago
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    @blackstreet23

  5. PinkSapphire
    • one year ago
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    For my answer, am I supposed to get rid of the square root in the denominator?

  6. blackstreet23
    • one year ago
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    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
    • one year ago
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    example \[1/\sqrt{2} \]

  8. PinkSapphire
    • one year ago
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    I think I did that, but I'm not sure that I understood you completely.

  9. blackstreet23
    • one year ago
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    hold on

  10. blackstreet23
    • one year ago
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    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
    • one year ago
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    that is the same as multiplying by one

  12. blackstreet23
    • one year ago
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    so you are not really changing the fraction itself, just how it looks

  13. blackstreet23
    • one year ago
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    is like if you get a hair cut, you may change how you look but you are still the same person.

  14. blackstreet23
    • one year ago
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    does that help a little?

  15. blackstreet23
    • one year ago
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    what have you done so far?

  16. PinkSapphire
    • one year ago
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    Okay, I think I did that.

  17. blackstreet23
    • one year ago
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    \[\frac{1 }{ \sqrt{2} } * \frac{ \sqrt{2} }{ \sqrt{2} }\]

  18. blackstreet23
    • one year ago
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    ohh ok.

  19. blackstreet23
    • one year ago
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    is that the answer on the back of the book?

  20. PinkSapphire
    • one year ago
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    What book?

  21. blackstreet23
    • one year ago
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    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
    • one year ago
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    Well, it is from my math book but we don't have the answers in the book.

  23. PinkSapphire
    • one year ago
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    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
    • one year ago
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    ohh just go to equation on the bottom of the text rectangle it has the sigma sign\[\sum_{}^{}\]

  25. blackstreet23
    • one year ago
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    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
    • one year ago
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    On the phone it doesn't have that.

  27. blackstreet23
    • one year ago
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    Could you use your phone as a hotspot so you use the phone's internet on your laptop?

  28. blackstreet23
    • one year ago
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    anyway, just write what you have using root(#)

  29. blackstreet23
    • one year ago
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    i will get it

  30. PinkSapphire
    • one year ago
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    I think I'll try it on the Safari app instead of the OpenStudy app.

  31. PinkSapphire
    • one year ago
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    I think I'll try it on the Safari app instead of the OpenStudy app.

  32. PinkSapphire
    • one year ago
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    No, it doesn't have it on there either.

  33. PinkSapphire
    • one year ago
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    It's working! Okay, this is the answer that I got:\[\frac{ \sqrt{11} }{ 10\sqrt{33} }\]

  34. blackstreet23
    • one year ago
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    just write it how i told you. I will try to get it :D

  35. blackstreet23
    • one year ago
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    ohh ok

  36. PinkSapphire
    • one year ago
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    Did you get a different answer?

  37. blackstreet23
    • one year ago
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    that is perfect so far

  38. blackstreet23
    • one year ago
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    but still incomplete

  39. blackstreet23
    • one year ago
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    you can factor it a little bit more

  40. blackstreet23
    • one year ago
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    what are the factors of 33?

  41. PinkSapphire
    • one year ago
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    3 and 11?

  42. blackstreet23
    • one year ago
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    yes. so what could cancel?

  43. PinkSapphire
    • one year ago
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    \[\sqrt{11}\]

  44. PinkSapphire
    • one year ago
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    Right?

  45. blackstreet23
    • one year ago
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    yes

  46. blackstreet23
    • one year ago
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    so what are you left with?

  47. PinkSapphire
    • one year ago
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    \[10\sqrt{3}\]

  48. PinkSapphire
    • one year ago
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    Right?

  49. blackstreet23
    • one year ago
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    actually \[1/10\sqrt{3}\]

  50. blackstreet23
    • one year ago
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    but yes

  51. blackstreet23
    • one year ago
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    and the last step is to do what i told you previously

  52. PinkSapphire
    • one year ago
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    Oh yeah, my mistake.

  53. blackstreet23
    • one year ago
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    make a fraction with the rational in the denominator of the first fraction. That fraction must equal to 1

  54. PinkSapphire
    • one year ago
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    I don't understand.

  55. blackstreet23
    • one year ago
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    which is the rational on the denominator of the fraction you have now?

  56. PinkSapphire
    • one year ago
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    \[\sqrt{3}\]

  57. blackstreet23
    • one year ago
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    so take that rational and make a fraction that equals 1

  58. blackstreet23
    • one year ago
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    do you know how to do it?

  59. blackstreet23
    • one year ago
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    \[\frac{ 5 }{ 5 }\]

  60. blackstreet23
    • one year ago
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    rings a bell?

  61. PinkSapphire
    • one year ago
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    How did you do that?

  62. blackstreet23
    • one year ago
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    ohh no i was just showing you that any number over itself equals one

  63. blackstreet23
    • one year ago
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    K/K = 1

  64. blackstreet23
    • one year ago
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    k = constant

  65. blackstreet23
    • one year ago
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    or any polynomial

  66. blackstreet23
    • one year ago
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    over itself is equal to 1

  67. blackstreet23
    • one year ago
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    so lets say

  68. blackstreet23
    • one year ago
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    \[\frac{ \sqrt{3} }{ \sqrt{3} } = 1\]

  69. PinkSapphire
    • one year ago
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    Okay...

  70. blackstreet23
    • one year ago
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    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
    • one year ago
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    you get it?

  72. PinkSapphire
    • one year ago
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    Not really. I'm sorry, but can you show it to me with numbers?

  73. blackstreet23
    • one year ago
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    you mean the concept that every number over itself equal 1 or how to finish your problem?

  74. PinkSapphire
    • one year ago
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    How to finish my problem.

  75. blackstreet23
    • one year ago
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    just multiply \[\frac{ \sqrt{3} }{ \sqrt{3} } * (previous fraction)\]

  76. blackstreet23
    • one year ago
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    that is what i meant

  77. mathstudent55
    • one year ago
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    |dw:1441502937030:dw|

  78. blackstreet23
    • one year ago
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    \[\frac{ \sqrt{3} }{\sqrt{3} } * \frac{ \sqrt{1} }{ 10\sqrt{3} }\]

  79. blackstreet23
    • one year ago
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    yes exactly

  80. mathstudent55
    • one year ago
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    \(\dfrac{ \sqrt 3 }{\sqrt 3 } \times \dfrac{ \color{red}{1} }{ 10\sqrt 3 }\)

  81. blackstreet23
    • one year ago
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    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
    • one year ago
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    You can also do it this way. |dw:1441503409900:dw|

  83. blackstreet23
    • one year ago
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    yes that is the answer \[\frac{ \sqrt{3} }{ 30 }\]

  84. PinkSapphire
    • one year ago
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    Okay, I get it. Thanks @blackstreet23 and @mathstudent55

  85. blackstreet23
    • one year ago
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    No problem, here to help :) good luck !

  86. mathstudent55
    • one year ago
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    You're welcome.

  87. PinkSapphire
    • one year ago
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    Thanks for taking the time to help me! :)

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