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anonymous

  • one year ago

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  1. anonymous
    • one year ago
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    \[\frac{ \sqrt{6} }{ \sqrt{5}-\sqrt{3} }\]

  2. anonymous
    • one year ago
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    Rationalize the denominator and simplify.

  3. Vocaloid
    • one year ago
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    the conjugate of the denominator is sqrt(5)+sqrt(3) (change the sign in the middle) \[\frac{ \sqrt{6} }{ \sqrt{5}-\sqrt{3}} * \frac{ \sqrt{5}+\sqrt{3} }{ \sqrt{5}+\sqrt{3}} \]

  4. Vocaloid
    • one year ago
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    multiply all of that out and simplify. there should be no radicals left in the denominator when you're done

  5. anonymous
    • one year ago
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    Ok well I think I'm left with \[\frac{ \sqrt{30}+\sqrt{18} }{ 2 }\] but I'm not sure if I did the math right.

  6. Vocaloid
    • one year ago
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    actually, yeah, that's right

  7. Vocaloid
    • one year ago
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    just know that you can simplify \[\sqrt{18} = 3\sqrt{2}\]

  8. Vocaloid
    • one year ago
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    but other than that you've got the answer

  9. anonymous
    • one year ago
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    Ok I'm not really sure how to simplify \[\sqrt{18}\] to get \[3\sqrt{2}\] is there a process to get there?

  10. Vocaloid
    • one year ago
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    \[\sqrt{18}=\sqrt{9*2}=\sqrt{3*3*2}=3\sqrt{2}\]

  11. anonymous
    • one year ago
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    So how would I do that to the \[\sqrt{30}\] or can't I? would it look like this: \[\sqrt{5*3*2}\]

  12. Vocaloid
    • one year ago
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    you can't, the square root of 30 is already simplified

  13. Vocaloid
    • one year ago
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    we can simplify the square root of 18 because it contains a perfect square (9) as a factor you can write square root of 30, no need to do anything else to it

  14. Vocaloid
    • one year ago
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    so your final answer would be \[\frac{ \sqrt{30}-3\sqrt{2} }{ 2 }\]

  15. anonymous
    • one year ago
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    Ok yeah I think I get it thank you.

  16. Vocaloid
    • one year ago
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    *small correction, there should be a plus sign in the numerator

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