anonymous
  • anonymous
how can you write the expression with a rationalized denominator? ^3sqrt2/^3sqrt4 ??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle \frac{\sqrt[3]{2} }{\sqrt[3]{4}} }\) like this?
anonymous
  • anonymous
Yes
SolomonZelman
  • SolomonZelman
Example problem 1: \(\large\color{#000000 }{ \displaystyle \frac{\sqrt[3]{3} }{\sqrt[3]{9}} }\) I know that, \(\large\color{#000000 }{ \displaystyle \sqrt[3]{9} \times \sqrt[3]{3}=\sqrt[3]{27}=3 }\) So, let's multiply times \(\large\color{#000000 }{ \displaystyle \sqrt[3]{3}}\) on top and bottom. \(\large\color{#000000 }{ \displaystyle \frac{\sqrt[3]{3} \times \sqrt[3]{3} }{\sqrt[3]{9}\times \sqrt[3]{3}} =\frac{\sqrt[3]{9}}{3} }\)

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anonymous
  • anonymous
Ok
SolomonZelman
  • SolomonZelman
Example problem 2: \(\color{#000000 }{ \displaystyle \frac{\sqrt[3]{4} }{\sqrt[3]{16}} }\) I know that, \(\color{#000000 }{ \displaystyle \sqrt[3]{16} \times \sqrt[3]{4}= \sqrt[3]{4^3}=4 }\) So, let's multiply times \(\large\color{#000000 }{ \displaystyle \sqrt[3]{4}}\) on top and bottom. \(\color{#000000 }{ \displaystyle \frac{\sqrt[3]{4} \times \sqrt[3]{4} }{\sqrt[3]{16}\times \sqrt[3]{4}} =\frac{\sqrt[3]{16}}{4} }\)
SolomonZelman
  • SolomonZelman
you are just multiplying (on top and bottom) times something that would make the denominator into integer, basically/
anonymous
  • anonymous
Ooh ok. So you would multiply the top by the bottom and get ^3sqrt 8
SolomonZelman
  • SolomonZelman
Wow
anonymous
  • anonymous
Wouldn't it just be 8?
SolomonZelman
  • SolomonZelman
Well, you are multiplying by \(\sqrt[3]{2}\), but not because it is the top, RATHER you are doing because that would (indeed) get you \(\sqrt[3]{8}=2\). And, you are multiplying times \(\sqrt[3]{2}\) on TOP and BOTTOM.
anonymous
  • anonymous
Oh ok.
SolomonZelman
  • SolomonZelman
|dw:1449366718019:dw|
anonymous
  • anonymous
Ooh ok I see
anonymous
  • anonymous
So would it come out to ^3sqrt4/2?
SolomonZelman
  • SolomonZelman
Yes, \(\displaystyle\frac{\sqrt[3]{4}}{2}\)
anonymous
  • anonymous
Ok awesome Thank you. I am so bad at math, sorry! I appreciate your help.
SolomonZelman
  • SolomonZelman
Anytime ...

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