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Schrodinger Group Title

I'm having trouble finding out how I can move from 4/(sqrt(2)-sqrt(6)) to -sqrt(2) - sqrt(6). I really can't figure this out for the life of me, and I have no idea why.

  • 2 years ago
  • 2 years ago

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  1. hartnn Group Title
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    hint :multiply and divide by (sqrt(2)+sqrt(6)

    • 2 years ago
  2. Schrodinger Group Title
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    I tried that, but i'm getting just a batsh*t crazy mess when I try to do that. I'm assuming you're talking about multiplying the numerator and denominator by the numerator? I must be doing something wrong there.

    • 2 years ago
  3. hartnn Group Title
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    not with numerator, with denominator, but with middle sign reversed , (sqrt(2)+sqrt(6)

    • 2 years ago
  4. Schrodinger Group Title
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    Okay, that's cool, but how do you just know to do that?

    • 2 years ago
  5. hartnn Group Title
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    its called rationalizing the denominator, if there is \(\large a+\sqrt b\) in the denominator, u multiply and divide by \(\large a-\sqrt b\)

    • 2 years ago
  6. hartnn Group Title
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    similar case when u want to rationalize the numerator.....

    • 2 years ago
  7. Schrodinger Group Title
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    Okay, cool. I've actually never seen that done before, at least formally, before. Thanks!

    • 2 years ago
  8. hartnn Group Title
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    welcome ^_^

    • 2 years ago
  9. hartnn Group Title
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    try it out here, and tell me if u don't get it....

    • 2 years ago
  10. Schrodinger Group Title
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    \[\frac{4}{\sqrt{2}-\sqrt{6}}\]... \[\frac{ 4 }{\sqrt{2}-\sqrt{6}} * \frac{ \sqrt{2}+\sqrt{6} }{ \sqrt{2}+\sqrt{6} }\]... \[\frac{ 4\sqrt{2}+4\sqrt{6} }{ 2+\sqrt{12}-\sqrt{12}-6 }\]... \[\frac{ 4\sqrt{2}+4\sqrt{6} }{ 2 - 6 }\]... \[\frac{ 4\sqrt{2}+4\sqrt{6} }{ -4 }\]... \[-\sqrt{2}-\sqrt{6}\] Correct?

    • 2 years ago
  11. hartnn Group Title
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    absolutely ! good work :)

    • 2 years ago
  12. Schrodinger Group Title
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    Thanks. I'm pretty worried/bothered at the fact that I was never formally taught that concept in middle or high school. My teachers were the type to kind of go, "Oh well you just put this here and do that and then hooray!" without giving a concrete or logically consistent approach to how to simplify or solve certain things. It's like it was assumed that I understood. Man, public school isn't exactly wonderful.

    • 2 years ago
  13. hartnn Group Title
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    don't worry, whatever u can't understand, ask here, we'll try our best to make u understand :)

    • 2 years ago
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