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

[Math100]

Homework Statement

None.

Relevant Equations

None.

Show sqrt(3), sqrt(5), sqrt(7), sqrt(24), and sqrt(31) are not rational numbers.

 

[PeroK]

These can all be done in one fell swoop if you think about it.

 

[Math100]

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?

 

[PeroK]

Can you please tell me what's that one fell swoop?

It means one proof to cover all those cases.

 

[THAUROS]

Hi, I wanted to share a link that I thought could help but I can't. Sorry!

 

[Math100]

It means one proof to cover all those cases.

What proof should/do I need to apply for this problem?

 

[PeroK]

What proof should/do I need to apply for this problem?

What's your proof for $\sqrt 3$? Can you generalise that?

 

[PeterDonis]

@Math100 please post your proof and equations directly in the thread using the PF LaTeX feature, not as a PDF.