Prove that $\sum_{i=2}^n \sqrt{i}$ is irrational for all $n \geq 2$
104917
Is $\sqrt1+\sqrt2+\dots+\sqrt n$ ever an integer?
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
63960
proving "e" irrational using convergent series
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
89716
Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
158066
Prove $2^{1/3}$ is irrational.
109953
How to prove that $\sqrt 3$ is an irrational number?
32848
Prove that the product of a non-zero rational and irrational number is irrational.
127830
proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
139755
Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
88429
Prove $\sqrt{2} + \sqrt{5}$ is irrational
17930
Please explain this step in proving the square root of 3 is irrational