anonymous
  • anonymous
rationalizing denominators, the cube root of 2y squared divided by the cube root of 9x squared
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
\[\frac{\sqrt[3]{2y}}{\sqrt[3]{9x^2}} \times \frac{\sqrt[3]{9x^2}}{\sqrt[3]{9x^2}}\]\[\implies\frac{\sqrt[3]{2y * 9x^2}}{9x^2}\] \[\implies\frac{\sqrt[3]{18yx^2}}{9x^2}\]
amistre64
  • amistre64
cbrt(9x^2)^2 does not equal 9x^2...
amistre64
  • amistre64
cbrt((3^2 x^2) times (cbrt(3x)) = 3x

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anonymous
  • anonymous
Sorry, I was thinking of a regular square root, thanks for catching that amistre. :P
amistre64
  • amistre64
no prob; happens to me all the time :)
amistre64
  • amistre64
trig test in 20mins...yawn :)
anonymous
  • anonymous
So the denominator should be \[\sqrt[3]{81x^4}\].
amistre64
  • amistre64
denom will rationalize to 3x
amistre64
  • amistre64
cbrt(3^2 x^2 3 x) = cbrt(3^3 x^3) = 3x
anonymous
  • anonymous
\[thats what I got but the answer \in the back of the book says cube \root of6xy squred divided by 3x\]
anonymous
  • anonymous
You're right. :P So the numerator should, in fact, be \[\sqrt[3]{6yx}\] and the denominator\[3x.\]
amistre64
  • amistre64
top: cbrt(2y) cbrt(3x) = cbrt(6xy) yep; checks out on my "mr proffesor"
radar
  • radar
Is it\[\sqrt[3]{(2y)2}\] or\[\sqrt[3]2y{2}\]
amistre64
  • amistre64
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anonymous
  • anonymous
how?
amistre64
  • amistre64
Ciao :)
radar
  • radar
The first expression is sort of confusing as it is written.
anonymous
  • anonymous
@abdon: If you multiply the denominator by cbrt(3x) you get cbrt(27*x^3) which simplifies to 3x. Now, because you multiplied the denominator by that factor, you have to multiply the numerator by the same factor, and you get cbrt(6xy).
radar
  • radar
My first post was just seeking clarification.
anonymous
  • anonymous
Ohhhhhhh, sorry, it is y^2...but that stays constant throughout, didn't see that before.
radar
  • radar
I am talking about the original problem posted by abdon
radar
  • radar
What is squared the 2y or just the y
anonymous
  • anonymous
I believe it was \[\sqrt[3]{2y^2}/\sqrt[3]{9x^2}.\]
radar
  • radar
OK. Thanks, now I will see if I get the same as you.
anonymous
  • anonymous
Sorry for having such broken up responses, here's the condensed form of what I got:\[\frac{\sqrt[3]{6xy^2}}{3x}.\]
anonymous
  • anonymous
\[got class ,thanks still confusing\]

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