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avai70178
 one year ago
I need some help rationalizing these denominators. Can anyone help?
avai70178
 one year ago
I need some help rationalizing these denominators. Can anyone help?

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avai70178
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 4 }{ 33\sqrt{2} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Multiply by the conjugate of the denominator \(3+\sqrt2\) divided by itself \[\frac{ 4 }{ 33\sqrt{2} }\times \frac{ 3+3\sqrt2 }{ 3+3\sqrt2}\]

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0wouldn't we multiply the top and bottom by \[3\sqrt{3}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no. you need to use the conjugate because it gives a difference of squares in the denominator and the radicals will cancel

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0okay so would we end up with \[\frac{ 12\sqrt{3} }{ 3 }\] ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no. It looks like you multiplied by something with √3. dw:1439590754304:dw

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0so what would we end up?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you have to do the multiplication

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0would the square root still be 2 in the numerator and be cancelled out in the denominator?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes. when you do FOIL on the denominator the middle terms will both have √2, but they'll have opposite signs and cancel.

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0oh okay give me a second to multiply

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0i feel like this is wrong but...\[\frac{ 12+12\sqrt{2} }{ 9 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's right. Now all you have to do is simplify it. 12 and 9 are both divisible by 3, so you reduce by dividing all those by 3

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0oh okay awesome so \[\frac{ 4+12\sqrt{2} }{ 3 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0both 12's so \[\frac{ 4+4\sqrt{2} }{ 3 }\]

avai70178
 one year ago
Best ResponseYou've already chosen the best response.0But thank you so much!
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