Is it possible that some combination of partial sums of $\sum \sqrt{k}$ be a rational number? $\text{where } k \text { not a perfect square}$

Asked Aug 17 '15 at 10:56

Active Nov 25 '16 at 06:28

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Is it possible that some combination of partial sums of $\sum \sqrt{k}$ be a rational number? $k=2,3,5,\cdots \text{where } k \text { not a perfect square}$

More ever : can a linear combination of $\sqrt[m_1]{k_1}$ , $\sqrt[m_2]{k_2}, \cdots$ be rational , where $k_i$ integer, is not perfect power of $m_i$? I.e. $k_i \neq a^{m_i}$ from some integer $a_i$?

edited Nov 25 '16 at 06:28

Martin Sleziak

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asked Aug 17 '15 at 10:56

jimjim

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1

You could search this site for questions tagged [rationality-testing] + [radicals]: http://math.stackexchange.com/questions/tagged/rationality-testing+radicals. Your first question has an answer here: http://math.stackexchange.com/a/437374/43288 – Bart Michels Aug 17 '15 at 11:02
@barto : thanks, does math.stackexchange.com/a/437374/43288 answer it for the case of square roots only? – jimjim Aug 17 '15 at 11:19

Is it possible that some combination of partial sums of $\sum \sqrt{k}$ be a rational number? $\text{where } k \text { not a perfect square}$

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