Proving the continued fraction expansion of $\sqrt2$
50930
Proving the continued fraction representation of $\sqrt{2}$
34491
Is there a way to show that $\sqrt{p_{n}} < n$?
62485
How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
87411
Prove that $\sqrt{x_1}+\sqrt{x_2}+\cdots+\sqrt{x_n} \geq (n-1) \left (\frac{1}{\sqrt{x_1}}+\frac{1}{\sqrt{x_2}}+\cdots+\frac{1}{\sqrt{x_n}} \right )$
125267
Prove that $2^{1/2}$ is irrational
31836
Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$
86603
Infinite square-rooting
17289
prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
142768
Approximation of $\sqrt{2}$
42842
Proof for $\epsilon$ closeness to $\sqrt{2}$ for all values of $\epsilon$
66082
Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$
132610
Expand $\sqrt{1-x}$ up to and including the term $x^2$ (How should i proceed further)
67605
Different proof that $\sqrt{2}$ is irrational
15205
Proving that the series 1 + ... + $1 / \sqrt{x}$ < $2 \sqrt{x}$
112595
Prove that the limit of this sequence is $\frac{1}{2}(1 + \sqrt{5})$