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

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

Well then there were no radicals in the denominator

5. anonymous

So u wld keep it the way it is

6. anonymous

really?

7. anonymous

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

8. anonymous

??

9. anonymous

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

10. anonymous

Ohh that is cool :P

11. anonymous

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

12. ParthKohli

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

13. anonymous

hmmm well u can be asked to rationalize the numerator too

14. anonymous

now im confused with the contradictions...

15. anonymous

16. anonymous

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

17. anonymous

Just use ur own brain -_-

18. anonymous

lol

19. anonymous

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.

21. anonymous

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

22. anonymous

rationalised

23. anonymous

i know what happens if it's in the denominator

24. anonymous

trust me lgba knows how to rationalize a numerator or denomanator

25. anonymous

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. anonymous

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. anonymous

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. anonymous

so why put in denominator then?

33. 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

34. anonymous

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. anonymous

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

37. anonymous
38. ParthKohli

Never rationalize the numerator unless given a question to perform.

39. anonymous
40. anonymous

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

41. anonymous

These are both reliable sources

42. anonymous

hmm

43. anonymous

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

44. anonymous

the links win. can't argue with that.

45. anonymous

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

46. anonymous

square roots in denominators really look weird...