## lgbasallote 3 years ago Rationalize: $\huge \frac{\sqrt{4+h} - 2}h$

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

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

3. lgbasallote

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

4. swissgirl

Well then there were no radicals in the denominator

5. swissgirl

So u wld keep it the way it is

6. lgbasallote

really?

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

8. lgbasallote

??

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

10. swissgirl

Ohh that is cool :P

11. lgbasallote

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

12. ParthKohli

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

13. swissgirl

hmmm well u can be asked to rationalize the numerator too

14. lgbasallote

now im confused with the contradictions...

15. swissgirl

16. lgbasallote

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

17. swissgirl

Just use ur own brain -_-

18. swissgirl

lol

19. lgbasallote

someone's wrong here....wonder who

20. 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.

$\frac{ 1 }{ \sqrt{2} }=\frac{ \sqrt{2} }{ 2 }$

rationalised

23. lgbasallote

i know what happens if it's in the denominator

24. swissgirl

trust me lgba knows how to rationalize a numerator or denomanator

25. lgbasallote

the question is if it's in the numerator

26. ParthKohli

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

27. ParthKohli

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

28. lgbasallote

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

29. ParthKohli

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

30. lgbasallote

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

31. ParthKohli

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

32. lgbasallote

so why put in denominator then?

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

34. 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

35. ParthKohli

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

36. lgbasallote

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

37. swissgirl
38. ParthKohli

Never rationalize the numerator unless given a question to perform.

39. swissgirl
40. lgbasallote

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

41. swissgirl

These are both reliable sources

42. lgbasallote

hmm

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

44. lgbasallote

the links win. can't argue with that.

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

46. lgbasallote

square roots in denominators really look weird...