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inverse
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Demonstrate that [itex]\sqrt{2}+\sqrt{3}[/itex] is irrational.
Thanks
Thanks
This feels like homework. However, I will give a proof just to make sure I still can:inverse said:Demonstrate that [itex]\sqrt{2}+\sqrt{3}[/itex] is irrational.
Thanks
inverse said:It is not to homwork, is to pass an exam.
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Norwegian said:Yes, probably homework, but we should not give misleading advice, so:
If Eval had done the first part correctly, he/she would have arrived at the otherwise immediate
√3 - √2 = m/n. Adding this equation to √3 + √2 = n/m, you obtain that √3 is rational, which is a contradiction.
Another way is just squaring both sides of √3 + √2 = n/m, giving √6 rational, and again a contradiction.
Eval said:If √3 + √2 = n/m, then 1/(√3 + √2) = m/n. Then, multiplying the top and bottom of the lefthand side by its conjugate, we get (√3 - √2)/(92+22) = (√3 - √2)/13 = m/n, not √3 - √2 = m/n.
An irrational demonstration is a scientific experiment or study that does not follow a logical or rational thought process. It may involve flawed reasoning, faulty data, or other factors that make it unreliable or invalid.
An irrational demonstration can be identified by looking for inconsistencies, logical fallacies, or gaps in the evidence. It may also be flagged if it contradicts well-established scientific principles or if it lacks peer review or replicability.
It is important to avoid irrational demonstrations because they can lead to false conclusions and potentially harm the scientific community's credibility. They can also waste time, resources, and funding that could be better used for valid and reliable research.
In some rare cases, an irrational demonstration may lead to unexpected discoveries or insights. However, these should be approached with caution and thoroughly tested and validated before being accepted as reliable evidence.
To prevent irrational demonstrations, scientists should follow strict research protocols, conduct thorough peer review, and aim for replicable results. It is also essential to remain open-minded and critical of one's own work to avoid biased or flawed thinking.