Question

RATIONALIZE THIS:

Answer 1

\[\frac{ \sqrt[3]{x + 24} - 3 }{ \sqrt{x + 1} - 2 }\]

Answer 2

I assume what you want is to get rid of the radical on the denominator?

Answer 3

so sorry for the late reply.

but yes.

Answer 4

Well, the trick I use here basically involves 'not caring about the numerator'

Put it this way: Generic fraction with a radical on the denominator...
\[\Large \frac{N}{\sqrt{r}\pm k}\]

Answer 5

N is the numerator (which I don't care about at the moment)
and we have \(\large \sqrt{r}\pm k\) in the denominator... and we want to remove the radical...
catch me so far?

Answer 6

yep. i tried that. actually I've reached this\[\frac{ \sqrt[3]{x+24-3} }{\sqrt{x+1}-2} \times \frac{ \sqrt[3]{x+24+3} }{\sqrt{x+1}+2} \times \frac{ \sqrt{x+1}+2 }{\sqrt{x+1}+2 }\]

Answer 7

yep. i understand you :)

Answer 8

Oh wait... something's wrong...

Answer 9

YOU paid attention to the numerator... I told you not to :P

All you do is multiply both the numerator and denominator by the *conjugate* of the denominator... (fancy word, but all it means is that you change the - to a +)

Answer 10

what? omg. sorry. we were taught to do that in school. Haha

Answer 11

its all about finding the limits. my answer was indeterminate so now, I had to like rationalize it or something

Answer 12

Oh... okay... then honestly, I don't know how to go about this... (something specific to your school instruction?)

Answer 13

Could you post the original question? :3