avai70178
  • avai70178
I need some help rationalizing these denominators. Can anyone help?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
avai70178
  • avai70178
\[\frac{ 4 }{ 3-3\sqrt{2} }\]
anonymous
  • anonymous
Multiply by the conjugate of the denominator \(3+\sqrt2\) divided by itself \[\frac{ 4 }{ 3-3\sqrt{2} }\times \frac{ 3+3\sqrt2 }{ 3+3\sqrt2}\]
avai70178
  • avai70178
wouldn't we multiply the top and bottom by \[-3\sqrt{3}\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
no. you need to use the conjugate because it gives a difference of squares in the denominator and the radicals will cancel
avai70178
  • avai70178
okay so would we end up with \[\frac{ 12\sqrt{3} }{ 3 }\] ?
anonymous
  • anonymous
no. It looks like you multiplied by something with √3. |dw:1439590754304:dw|
avai70178
  • avai70178
so what would we end up?
anonymous
  • anonymous
you have to do the multiplication
avai70178
  • avai70178
would the square root still be 2 in the numerator and be cancelled out in the denominator?
anonymous
  • anonymous
yes. when you do FOIL on the denominator the middle terms will both have √2, but they'll have opposite signs and cancel.
avai70178
  • avai70178
oh okay give me a second to multiply
avai70178
  • avai70178
i feel like this is wrong but...\[\frac{ 12+12\sqrt{2} }{ -9 }\]
anonymous
  • anonymous
That'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
  • avai70178
oh okay awesome so \[\frac{ 4+12\sqrt{2} }{ -3 }\]
anonymous
  • anonymous
both 12's so \[\frac{ 4+4\sqrt{2} }{ -3 }\]
avai70178
  • avai70178
oh my bad sorry
avai70178
  • avai70178
But thank you so much!
anonymous
  • anonymous
you're welcome

Looking for something else?

Not the answer you are looking for? Search for more explanations.