Prove that $1+\sqrt{2}+\sqrt{3}+\dots+\sqrt{n}$ is irrational for every natural number $n\ge2$.
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2Hint: There is some largest prime number in the set ${1,2,\dots,n}$ – JMoravitz Jan 06 '18 at 22:02
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Some reference paper: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.630.1024&rep=rep1&type=pdf – zwim Jan 06 '18 at 22:14