      # Rationalize

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### #1 James Noel

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Posted 25 December 2009 - 06:02 PM

Hi there, can anyone tell me if there is a way that I can make cp rationalize. I mean is there an trick up your sleeves/ Thank you very much in advance

### #2 ASTRO491K

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Posted 26 December 2009 - 05:50 AM

Could you be more specific and offer an example problem of what you have in mind?

### #3 James Noel

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Posted 26 December 2009 - 11:15 AM

Could you be more specific and offer an example problem of what you have in mind?

Hi, if you are still there this would be an example:
x/(x^2-1)^(1/2)

### #4 ASTRO491K

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Posted 26 December 2009 - 06:34 PM

Hi, if you are still there this would be an example:
x/(x^2-1)^(1/2)

In mathematics, to rationalize means to express without a radical sign. We commonly simpliy expressions by rationalizing either a numberator or more commonly the denominator. In your case, multiplying both the numerator and denominator by (x^2-1)^(1/2) will rationalize the denominator without changing the value of the expression with the result of x((x^2-1)^(1/2))/(x^2-1). We have simply changed the form of the expression. A more common and slightly more difficult problem would be to rationalize the denominator of x/(x^(1/2)-1) which is rationalized by multiplying the numerator and denominator by (x^(1/2)+1). For this example the result is x((x^(1/2)+1))/(x-1). Notice that there is no longer a square root in the denominator.

### #5 James Noel

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Posted 29 December 2009 - 02:23 AM

In mathematics, to rationalize means to express without a radical sign. We commonly simpliy expressions by rationalizing either a numberator or more commonly the denominator. In your case, multiplying both the numerator and denominator by (x^2-1)^(1/2) will rationalize the denominator without changing the value of the expression with the result of x((x^2-1)^(1/2))/(x^2-1). We have simply changed the form of the expression. A more common and slightly more difficult problem would be to rationalize the denominator of x/(x^(1/2)-1) which is rationalized by multiplying the numerator and denominator by (x^(1/2)+1). For this example the result is x((x^(1/2)+1))/(x-1). Notice that there is no longer a square root in the denominator.

I understand what it is to rationalize. I just want to know if the calc can do it so that I can get more thorough working out of certain answers. If not, I guese its just another one of classpad limitations. Now I know there are other calc that can do that though.

Edited by James Noel, 29 December 2009 - 02:31 AM.

### #6 ASTRO491K

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Posted 29 December 2009 - 05:46 AM

I understand what it is to rationalize. I just want to know if the calc can do it so that I can get more thorough working out of certain answers. If not, I guese its just another one of classpad limitations. Now I know there are other calc that can do that though.

Mr. Noel, Think closely about what I am about to tell you because it is very important. The question is not can the calculator rationalize an expression, the question is can you operate the calculator in such a fashion so as to rationalize an expression. Yes, the calculator has the skills to rationalize because it has the ability to do algebraic multiplication, but you must have the skills to operate it properly in order to do the rationalization and that means you must be able to tell it what to multiply by.

To dig deeper, the whole point of having a calculator is to use it to do the math that you know how to do, but use the calculator to allow you to do that math more quickly and accruately. What I am saying is that you are in control of the machine so if you can not do the math without the machine, then by using the machine, you most certainly will not be able to do the math more quickly and accurately. A calculator is not a magic box that can, or should be able to, do any math problem you pose to it. A calculator simply caries out operations that are asked of it. So you need to learn enough math to be able to operate the calculator properly. If you cannot do that, then the calculator under your control cannot do it either.

Having said all that, my sense it that you want to substitute calculator button pushing for doing mathematics. That would be a big mistake because any idiot can get an answer by pushing buttons, but it takes a mathematician to push the right buttons in the right order to end up with the "correct" answer. And that takes me back to the starting point. Your calculator can do algebraic multiplication, so can you use it to do rationalization? If not, the fault is not with the calculator but with you.

### #7 James Noel

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Posted 29 December 2009 - 10:31 PM

Mr. Noel, Think closely about what I am about to tell you because it is very important. The question is not can the calculator rationalize an expression, the question is can you operate the calculator in such a fashion so as to rationalize an expression. Yes, the calculator has the skills to rationalize because it has the ability to do algebraic multiplication, but you must have the skills to operate it properly in order to do the rationalization and that means you must be able to tell it what to multiply by.

To dig deeper, the whole point of having a calculator is to use it to do the math that you know how to do, but use the calculator to allow you to do that math more quickly and accruately. What I am saying is that you are in control of the machine so if you can not do the math without the machine, then by using the machine, you most certainly will not be able to do the math more quickly and accurately. A calculator is not a magic box that can, or should be able to, do any math problem you pose to it. A calculator simply caries out operations that are asked of it. So you need to learn enough math to be able to operate the calculator properly. If you cannot do that, then the calculator under your control cannot do it either.

Having said all that, my sense it that you want to substitute calculator button pushing for doing mathematics. That would be a big mistake because any idiot can get an answer by pushing buttons, but it takes a mathematician to push the right buttons in the right order to end up with the "correct" answer. And that takes me back to the starting point. Your calculator can do algebraic multiplication, so can you use it to do rationalization? If not, the fault is not with the calculator but with you.

Hi,
its me again, I don't want to use the calculator to do all the mathematics for me but rather to understands its limitations. I think it is safe to say that one must understand the limitation of ones tool so that one can better appreciate its use more. Already I have an undersand most of the limitation. I realized that it can do rationalization, I just use the simplify option on the pull down menu. You see the whole question is to what degree. In my observation, I discover that Hp can do rationalization very well in comparason to Classpad (not to mention there are quite a few things Classpad can do that Hp 50g cannot do and vice vera).
There are some things that I thought Classpad cannot do, only to realize that yes indeed it can do them but just in a totally different way, different to even to its predecessors. I am not upset about that, it just excites me to learn more. I have read the manual before I baught it. I read other learning material on Classpad. You must understand it is not just a spur of the moment realization.
I discover that it does not rationalize symbols very well e.g. x/(squar(2x-1)). Just wonder if there is a way around that or thats just it. If so, then thats one of its limitation. I know that the Hp can, and other examples like the one I gave.
When I read the real world reviews in this forum and how far the unit has come from when it first hit the market. I have to ask these questions. This the best calculator that Casio has. There are always going to be question like these, and should be in my opinion. I mean, is it a worthy purchase? It is a learning tool, that is what its has been advertised as mostly. Therefore it takes on a different "persona" just like the Nspire and maybe a few others. when I first got it I thought I would do some calculous problem step by step. I am not to dissapointed since I know that in most advertising there has to be a certaind degree of hype. But the basic thing like working a calculous problem to it completion is what worries me a bit. For instance that example is an incomplete answer an answer that should be rationalized further. Not to mention it cost considerably more than Hp 50g. I figure that is the case since this is fairly new unit and is in a different class (Learning tool). The fact that it is advertized as a learning tool, saids a lot.
I don't think that I should be humbled by the type question I asked about Classpad in fear that it may qualify my intelegence and understanding about Mathematics in general. I think questions like these will always arise.

Edited by James Noel, 29 December 2009 - 11:15 PM.

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