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julia_copen

  • 2 years ago

Help with this last radical?

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  1. jim_thompson5910
    • 2 years ago
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    what's your question

  2. julia_copen
    • 2 years ago
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    Hang on a second

  3. jim_thompson5910
    • 2 years ago
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    ok

  4. julia_copen
    • 2 years ago
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    I have to draw it lol

  5. jim_thompson5910
    • 2 years ago
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    you're fine, no worries

  6. jim_thompson5910
    • 2 years ago
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    that's definitely the best option instead of describing it in words

  7. julia_copen
    • 2 years ago
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    It isn't working. I have no idea what to do.

  8. julia_copen
    • 2 years ago
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    |dw:1364269301720:dw|

  9. jim_thompson5910
    • 2 years ago
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    ok one sec

  10. julia_copen
    • 2 years ago
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    OK my drawing sucks but this is it.

  11. jim_thompson5910
    • 2 years ago
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    thanks, and your drawing is perfect, no worries

  12. jim_thompson5910
    • 2 years ago
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    you need to rationalize the denominator, so you need to multiply top and bottom by \[\Large 10\sqrt{2} + \sqrt{10}\]

  13. jim_thompson5910
    • 2 years ago
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    Doing so will give you \[\Large \frac{5\sqrt{2}+\sqrt{10}}{10\sqrt{2} - \sqrt{10}}\] \[\Large \frac{(5\sqrt{2}+\sqrt{10})((10\sqrt{2} + \sqrt{10}))}{(10\sqrt{2} - \sqrt{10})(10\sqrt{2} + \sqrt{10})}\] Do you know what to do from here?

  14. julia_copen
    • 2 years ago
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    No this is where I got lost.

  15. jim_thompson5910
    • 2 years ago
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    ok you would use the difference of squares rule to expand out the denominator \[\Large (10\sqrt{2} - \sqrt{10})(10\sqrt{2} + \sqrt{10})\] \[\Large (10\sqrt{2})^2 - (\sqrt{10})^2\] \[\Large 10^2*(\sqrt{2})^2 - (\sqrt{10})^2\] \[\Large 100*2 - 10\] \[\Large 200 - 10\] \[\Large 190\]

  16. jim_thompson5910
    • 2 years ago
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    So \[\Large \frac{(5\sqrt{2}+\sqrt{10})((10\sqrt{2} + \sqrt{10}))}{(10\sqrt{2} - \sqrt{10})(10\sqrt{2} + \sqrt{10})}\] turns into \[\Large \frac{(5\sqrt{2}+\sqrt{10})((10\sqrt{2} + \sqrt{10}))}{190}\]

  17. jim_thompson5910
    • 2 years ago
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    You just need to expand out the numerator, then you're done

  18. jim_thompson5910
    • 2 years ago
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    Doing that will give you \[\Large (5\sqrt{2}+\sqrt{10})(10\sqrt{2} + \sqrt{10})\] \[\Large 5\sqrt{2}(10\sqrt{2} + \sqrt{10})+\sqrt{10}(10\sqrt{2} + \sqrt{10})\] \[\Large 5\sqrt{2}*10\sqrt{2} + 5\sqrt{2}*\sqrt{10}+\sqrt{10}*10\sqrt{2} + \sqrt{10}*\sqrt{10}\] \[\Large 100 + 5\sqrt{20}+10\sqrt{20} + 10\] \[\Large 110 + 15\sqrt{20}\] \[\Large 110 + 15\sqrt{4*5}\] \[\Large 110 + 15\sqrt{4}*\sqrt{5}\] \[\Large 110 + 15*2*\sqrt{5}\] \[\Large 110 + 30*\sqrt{5}\]

  19. jim_thompson5910
    • 2 years ago
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    So \[\Large \frac{(5\sqrt{2}+\sqrt{10})((10\sqrt{2} + \sqrt{10}))}{190}\] turns into \[\Large \frac{110 + 30*\sqrt{5}}{190}\] I guess from here you can divide each term by 10 to get \[\Large \frac{11 + 3\sqrt{5}}{19}\] and you're done

  20. jim_thompson5910
    • 2 years ago
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    So this shows us that \[\Large \frac{5\sqrt{2}+\sqrt{10}}{10\sqrt{2} - \sqrt{10}} =\frac{11 + 3\sqrt{5}}{19}\]

  21. julia_copen
    • 2 years ago
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    Neat. You explained it so well! I wouldn't have been able to foil that like you did. Thanks!

  22. jim_thompson5910
    • 2 years ago
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    you're welcome

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