anonymous
  • anonymous
Write each expression in lowest terms. Assume that all variables represent positive real numbers:(6p+√24p^3)/3p
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{ 6p+\sqrt{24p ^{3}} }{ 3p }\]
anonymous
  • anonymous
That is how it is set up, it says I'm suppose to factor the numerator and denominator. The denominator ends up being 3 alone and the numerator looks like: 6+2√6p in the answer key, so the two p's must cancel on top and bottom, but where does the cube go?
anonymous
  • anonymous
since \(\sqrt{24}=\sqrt{4\times 6}=\sqrt{4}\sqrt{6}=2\sqrt{6}\) and \(\sqrt{p^3}=p\sqrt{p}\) you can start with \[\frac{6p+2\sqrt{6p}}{3p}\]

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anonymous
  • anonymous
oops i meant start with \[\frac{6p+2p\sqrt{6p}}{3p}\]
anonymous
  • anonymous
then factor out the common factor of \(p\) and cancel it with the one in the denominator
anonymous
  • anonymous
Thank you! I appreciate your help! I see how it is done now.

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