Prove $\sqrt{x}$ is irrational if $n^2 \lt x \lt (n+1)^2$.
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
96204
Irrational number $\sqrt2$ proof
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
60036
How to prove this limit exists: $a_{n+2}=\sqrt{a_{n+1}}+\sqrt{a_{n}}$
50930
Proving the continued fraction representation of $\sqrt{2}$
59475
Show that $\sqrt{n+1}-\sqrt{n}\to0$
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
144244
Bound on difference between irrational square root and rational number
30478
How to prove that a number is irrational
44391
How can I prove $n - 2\sqrt{n} = \Theta(n)$
87596
Is $\sum_{p}\frac{1}{p^{2}}$ irrational?
100973
Check if this proof about real numbers with an irrational product is correct.
32
Is $n^{th}$ root of $2$ an irrational number?
148582
Proof: $\|X\|_2\leq \sqrt{n}\|X\|_\infty$
100375
Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
139755
Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.