Can $\sum_{n=2}^{k} \sqrt{n}$ be rational?
104917
Is $\sqrt1+\sqrt2+\dots+\sqrt n$ ever an integer?
101052
Find the infinite sum $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $
56802
Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
95459
$\mathbb{Q}(\sqrt{2+\sqrt{2}})$ is Galois over $\mathbb{Q}$?
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
137155
Sum $ \sum\limits_{k=1}^{\infty} \frac{k^2}{2^k}$
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
88429
Prove $\sqrt{2} + \sqrt{5}$ is irrational
89716
Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
90276
Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
132931
Determining the parity of the coefficients of a quadratic given that there is a rational solution
117132
Rationals of the form $\frac{p}{q}$ where $p,q$ are primes in $[a,b]$
98808
Finite Sum $\sum_{i=1}^n\frac i {2^i}$
76867
Does $\sum _{k=2} ^\infty \frac{(-1)^k}{\sqrt{k}+(-1)^k}$ converge conditionally?
139755
Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
56877
Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational.