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$\sqrt{a_1}, \sqrt{a_2} ,\cdots, \sqrt{a_n}$ are irrationals and $a_1,a_2,\cdots,a_n$ are integers $>1$.
I didn't find any proof for this exercise. Please help!!

Bumblebee
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Jonutz123
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  • what are you asking? – dmtri Sep 24 '19 at 19:05
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    It would seem you didn't learn anything from your previous question, and still haven't shown any effort to your questions. If you had a question about something specific from the proofs in the duplicates to your previous question, you should ask them instead. – Simply Beautiful Art Sep 24 '19 at 19:16
  • This might be useful for you next time. https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – Bumblebee Sep 24 '19 at 23:11

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Counter example: $$\sqrt{7-4\sqrt3}+\sqrt{7+4\sqrt3}=4$$

Bumblebee
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  • That's just $(2-\sqrt 3)+(2+\sqrt 3)$. I realise the question doesn't explicitly rule out such counter-examples, but the obvious unstated assumption is that the $a_i$ are rational. (And I see that while I was writing this, the OP has made this explicit.) – TonyK Sep 24 '19 at 19:13
  • Exactly. The given conclusion does not follows from the given hypothesis. – Bumblebee Sep 24 '19 at 19:18
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    @Bumblebee Unfortunately, an initial edit by another user to add MathJax accidentally removed the OP's explicit statement the $a_i$ were integers $ \gt 1$. The later edit by the OP put this requirement back into the question text. – John Omielan Sep 24 '19 at 23:00
  • @JohnOmielan: Thank you for the information. – Bumblebee Sep 24 '19 at 23:10