anonymous
  • anonymous
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Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{ \sqrt{6} }{ \sqrt{5}-\sqrt{3} }\]
anonymous
  • anonymous
Rationalize the denominator and simplify.
Vocaloid
  • Vocaloid
the conjugate of the denominator is sqrt(5)+sqrt(3) (change the sign in the middle) \[\frac{ \sqrt{6} }{ \sqrt{5}-\sqrt{3}} * \frac{ \sqrt{5}+\sqrt{3} }{ \sqrt{5}+\sqrt{3}} \]

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Vocaloid
  • Vocaloid
multiply all of that out and simplify. there should be no radicals left in the denominator when you're done
anonymous
  • anonymous
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.
Vocaloid
  • Vocaloid
actually, yeah, that's right
Vocaloid
  • Vocaloid
just know that you can simplify \[\sqrt{18} = 3\sqrt{2}\]
Vocaloid
  • Vocaloid
but other than that you've got the answer
anonymous
  • anonymous
Ok I'm not really sure how to simplify \[\sqrt{18}\] to get \[3\sqrt{2}\] is there a process to get there?
Vocaloid
  • Vocaloid
\[\sqrt{18}=\sqrt{9*2}=\sqrt{3*3*2}=3\sqrt{2}\]
anonymous
  • anonymous
So how would I do that to the \[\sqrt{30}\] or can't I? would it look like this: \[\sqrt{5*3*2}\]
Vocaloid
  • Vocaloid
you can't, the square root of 30 is already simplified
Vocaloid
  • Vocaloid
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
Vocaloid
  • Vocaloid
so your final answer would be \[\frac{ \sqrt{30}-3\sqrt{2} }{ 2 }\]
anonymous
  • anonymous
Ok yeah I think I get it thank you.
Vocaloid
  • Vocaloid
*small correction, there should be a plus sign in the numerator

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