Can anyone please check/verify this proof about rational numbers?

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The discussion revolves around proving that the square roots of 3, 5, 7, 24, and 31 are not rational numbers. Participants are seeking a unified proof that can address all these cases simultaneously. There is a request for specific proof techniques, particularly for √3, and a suggestion to use the PF LaTeX feature for clarity. The conversation emphasizes the need for a generalizable approach to demonstrate the irrationality of these square roots. Overall, the focus is on finding an efficient proof method applicable to multiple examples.
Math100
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Homework Statement
None.
Relevant Equations
None.
Show sqrt(3), sqrt(5), sqrt(7), sqrt(24), and sqrt(31) are not rational numbers.
 

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These can all be done in one fell swoop if you think about it.
 
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PeroK said:
These can all be done in one fell swoop if you think about it.
Can you please tell me what's that one fell swoop?
 
Math100 said:
Can you please tell me what's that one fell swoop?
It means one proof to cover all those cases.
 
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THAUROS said:
Hi, I wanted to share a link that I thought could help but I can't. Sorry!
 
PeroK said:
It means one proof to cover all those cases.
What proof should/do I need to apply for this problem?
 
Math100 said:
What proof should/do I need to apply for this problem?
What's your proof for ##\sqrt 3##? Can you generalise that?
 
@Math100 please post your proof and equations directly in the thread using the PF LaTeX feature, not as a PDF.
 

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