anonymous
  • anonymous
Help with this last radical?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
jim_thompson5910
  • jim_thompson5910
what's your question
anonymous
  • anonymous
Hang on a second
jim_thompson5910
  • jim_thompson5910
ok

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anonymous
  • anonymous
I have to draw it lol
jim_thompson5910
  • jim_thompson5910
you're fine, no worries
jim_thompson5910
  • jim_thompson5910
that's definitely the best option instead of describing it in words
anonymous
  • anonymous
It isn't working. I have no idea what to do.
anonymous
  • anonymous
|dw:1364269301720:dw|
jim_thompson5910
  • jim_thompson5910
ok one sec
anonymous
  • anonymous
OK my drawing sucks but this is it.
jim_thompson5910
  • jim_thompson5910
thanks, and your drawing is perfect, no worries
jim_thompson5910
  • jim_thompson5910
you need to rationalize the denominator, so you need to multiply top and bottom by \[\Large 10\sqrt{2} + \sqrt{10}\]
jim_thompson5910
  • jim_thompson5910
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?
anonymous
  • anonymous
No this is where I got lost.
jim_thompson5910
  • jim_thompson5910
ok you would use the difference of squares rule to expand out the denominator \[\Large (10\sqrt{2} - \sqrt{10})(10\sqrt{2} + \sqrt{10})\] \[\Large (10\sqrt{2})^2 - (\sqrt{10})^2\] \[\Large 10^2*(\sqrt{2})^2 - (\sqrt{10})^2\] \[\Large 100*2 - 10\] \[\Large 200 - 10\] \[\Large 190\]
jim_thompson5910
  • jim_thompson5910
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 \[\Large \frac{(5\sqrt{2}+\sqrt{10})((10\sqrt{2} + \sqrt{10}))}{190}\]
jim_thompson5910
  • jim_thompson5910
You just need to expand out the numerator, then you're done
jim_thompson5910
  • jim_thompson5910
Doing that will give you \[\Large (5\sqrt{2}+\sqrt{10})(10\sqrt{2} + \sqrt{10})\] \[\Large 5\sqrt{2}(10\sqrt{2} + \sqrt{10})+\sqrt{10}(10\sqrt{2} + \sqrt{10})\] \[\Large 5\sqrt{2}*10\sqrt{2} + 5\sqrt{2}*\sqrt{10}+\sqrt{10}*10\sqrt{2} + \sqrt{10}*\sqrt{10}\] \[\Large 100 + 5\sqrt{20}+10\sqrt{20} + 10\] \[\Large 110 + 15\sqrt{20}\] \[\Large 110 + 15\sqrt{4*5}\] \[\Large 110 + 15\sqrt{4}*\sqrt{5}\] \[\Large 110 + 15*2*\sqrt{5}\] \[\Large 110 + 30*\sqrt{5}\]
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
So this shows us that \[\Large \frac{5\sqrt{2}+\sqrt{10}}{10\sqrt{2} - \sqrt{10}} =\frac{11 + 3\sqrt{5}}{19}\]
anonymous
  • anonymous
Neat. You explained it so well! I wouldn't have been able to foil that like you did. Thanks!
jim_thompson5910
  • jim_thompson5910
you're welcome

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