Halo

Hello How do you show that there are no whole numbers [math]n[/math], [math]m[/math], [math]n\times m\neq 0[/math] such that [math]m\sqrt{2}+n\sqrt{2}[/math] is a rational number. Thanks!

Hello These notes were taken from a lecture I had the other day: [math]\sum\limits_{k=0}^m \binom{m}{k}x^k + \sum\limits_{k=0}^m \binom{m}{k}x^{k+1}[/math] [math]= \sum\limits_{k=0}^m \binom{m}{k}x^k + \sum\limits_{k}^{m+k} \binom{m}{k}x^{k(k+1)}[/math] [math]= \binom{m}{0}x^0 + \sum\limits_{k=1}^m (\binom{m}{k} + \binom{m}{k-1})x^k + \binom{m}{m}x^{m+1}[/math] [math]= 1 + \sum\limits_{k=1}^m \binom{m+1}{k}x^k + x^{n+1}[/math] [math]= \sum\limits_{k=0}^{m+1} \binom{m+1}{k}x^k[/math] Can someone please explain to me by which rules these steps are possible, because it is all greek to me at the moment. The steps are part of a proof for the Binomial Theorem. Thanks in advance!

Ok, It has been a while since I posted this. I have measured the activity of gamma rays, when it has passed throught different thickness of some material, like lead and copper for example. This means that I now have the initial activity as well as the decreasing activity, along with thicker material. Would plotting these numbers in a graf make any sense, or how should I make use of them?

Tomorrow I am going to measure how well different material is stopping beta and gamma radiation. I have not done this before, so what I need to know is, how do you use a Geiger counter? Do you simply plug it in or do you have to adjust something on it first? I would appreciate any help. Thanks in advance!

Hello I am writing a project about inozing radiation. The aim of the project is to examine the nature of alpha, beta and gamma radiation and describe how they differ. As for now I have been blessed with good information from litterature and I have written a lot. However, I have got myself in a bit of a situation: My project is supposed to include practical measurings of radiation, where I measure some physical quantities of the radiation and compare them to the other radiations. The problem is I do not know what "physical quantities" I can measure and how to put the numbers I get in a context. For example the activity is "easy" to measure, or so I have heard, but I do not think the activity have anything to do with the ionizing radiation itself. The only thing I can think of is measuring their respective energies in a mass spectrometer. It does not have to be physical quantities, instead it could be characteristics, like for example what objects they can go throught. Any help on how I should do this would be greatly appreciated.