Prove or disprove: $\sqrt{2\sqrt{3\sqrt{4\sqrt{\ldots\sqrt{n}}}}}<3$
108588
Improving bound on $\sqrt{2 \sqrt{3 \sqrt{4 \ldots}}}$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
127102
Upper bound for $\sqrt[n]{n!}$
19804
How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
52157
Prove that $d(n)\leq 2\sqrt{n}$
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
4333
Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$
115454
Primality test bound: square root of n
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
56420
Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
30622
Proving $\sqrt 3$ is irrational.
34767
Proving $\left(1+\dfrac{1}{1^3}\right)\left(1+\dfrac{1}{2^3}\right)\cdots\left(1+\dfrac{1}{n^3}\right)<3$ for all positive integers $n$
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
117046
Show that $\frac{a^2}{\sqrt{(1+a^3)(1+b^3)}}+\frac{b^2}{\sqrt{(1+b^3)(1+c^3)}}+\frac{c^2}{\sqrt{(1+c^3)(1+a^3)}} \geq \frac{4}{3}$
117970
Find the minimal polynomial for $\sqrt[3]{2} + \sqrt[3]{4}$ over $\mathbb{Q}$