Rationalize:
\[\huge \frac{\sqrt{4+h} - 2}h\]

- lgbasallote

Rationalize:
\[\huge \frac{\sqrt{4+h} - 2}h\]

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- anonymous

\[\frac{ 4+h-4 }{ h(\sqrt{4+h}+2) }=\frac{ 1 }{\sqrt{4+h}+2 }\]
nomarlly limit question

- anonymous

we multiplied by\[\sqrt{4+h}+2\]
both num and denominator

- lgbasallote

hmmm...isn't the point of rationalization to remove radicals from the denominator?

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## More answers

- swissgirl

Well then there were no radicals in the denominator

- swissgirl

So u wld keep it the way it is

- lgbasallote

really?

- anonymous

imagine if this question was\[\lim_{h \rightarrow 0}\frac{ \sqrt{4+h}-2 }{ h }\]

- lgbasallote

??

- anonymous

you cant just plug h=0 here but in the rationalised one

- swissgirl

Ohh that is cool :P

- lgbasallote

limits in an algebra question? that's morbid.....

- ParthKohli

Rationalizing means to remove the radical from the place it is in...

- swissgirl

hmmm well u can be asked to rationalize the numerator too

- lgbasallote

now im confused with the contradictions...

- swissgirl

What are the contradictions?

- lgbasallote

@swissgirl said don't change...now she says change

- swissgirl

Just use ur own brain -_-

- swissgirl

lol

- lgbasallote

someone's wrong here....wonder who

- ParthKohli

If they ask you to rationalize the fraction, you do these:
1) If the radical is in the denominator — remove it from the denominator. Do not care about the numerator.
2) If the radical is in the numerator — remove it from the numerator. Do not care about the denominator.

- anonymous

\[\frac{ 1 }{ \sqrt{2} }=\frac{ \sqrt{2} }{ 2 }\]

- anonymous

rationalised

- lgbasallote

i know what happens if it's in the denominator

- swissgirl

trust me lgba knows how to rationalize a numerator or denomanator

- lgbasallote

the question is if it's in the numerator

- ParthKohli

See how you can't remove the radical from both numerator and denominator?

- ParthKohli

Yes, so move it to the denominator. Do not care about the denominator.

- lgbasallote

my question is not how to rationalize @swissgirl but if it's suppose to be rationalized

- ParthKohli

You can rationalize it, but mathematicians always love if the radical is in the numerator.

- lgbasallote

because what i know is that if it's in the numerator, then it's okay

- ParthKohli

It's better to put radicals in the numerator rather than the denominator.

- lgbasallote

so why put in denominator then?

- anonymous

\[\frac{ \sqrt{2} }{ 2 }=\frac{ 1 }{ \sqrt{2} }\]
these is also called rationalising sometimes it is convinient to write in the dinominatpr eg in the case of a limit

- swissgirl

Well what i have always learnt was that rationalization=denominator but I have gone online and seen that some do rationalize the numerator too so it all depends what course you are taking and what you see in your the textbook

- ParthKohli

Yup, I saw that you could rationalize the numerator too though it's rare.

- lgbasallote

when i went online, all i saw were unreliable sources on rationalizing numerators

- swissgirl

http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut41_rationalize.htm

- ParthKohli

Never rationalize the numerator unless given a question to perform.

- swissgirl

http://tutorial.math.lamar.edu/Extras/AlgebraTrigReview/Rationalizing.aspx

- lgbasallote

\[\lim_{x \rightarrow 0} \sqrt x\]seems better than \[\lim_{x \rightarrow 0} \frac 1{\sqrt x}\]
@Jonask

- swissgirl

These are both reliable sources

- lgbasallote

hmm

- anonymous

how ever if you where asked to do the same function using the first prinsiple you will need to rationalise

- lgbasallote

the links win. can't argue with that.

- anonymous

\[\frac{ \sqrt{x+h}-\sqrt{x} }{ h }\]ration.
\[\frac{ 1 }{ \sqrt{x+h}+\sqrt{x} }\]

- lgbasallote

square roots in denominators really look weird...

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