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Demonstrate that [itex]\sqrt{2}+\sqrt{3}[/itex] is irrational.
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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)/(9^{2}+2^{2}) = (√3 - √2)/13 = m/n, not √3 - √2 = m/n.