Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

Well then there were no radicals in the denominator

Answer 5

So u wld keep it the way it is

Answer 6

really?

Answer 7

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

Answer 8

??

Answer 9

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

Answer 10

Ohh that is cool :P

Answer 11

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

Answer 12

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

Answer 13

hmmm well u can be asked to rationalize the numerator too

Answer 14

now im confused with the contradictions...

Answer 15

What are the contradictions?

Answer 16

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

Answer 17

Just use ur own brain -_-

Answer 18

lol

Answer 19

someone's wrong here....wonder who

Answer 20

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.

Answer 21

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

Answer 22

rationalised

Answer 23

i know what happens if it's in the denominator

Answer 24

trust me lgba knows how to rationalize a numerator or denomanator

Answer 25

the question is if it's in the numerator

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

so why put in denominator then?

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

Never rationalize the numerator unless given a question to perform.

Answer 39

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

Answer 40

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

Answer 41

These are both reliable sources

Answer 42

hmm

Answer 43

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

Answer 44

the links win. can't argue with that.

Answer 45

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

Answer 46

square roots in denominators really look weird...