prove that $\sqrt{x+1} \gt \sqrt{x}$ if $x \gt 1$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
55266
Prove that $(n+1)^{n-1}<n^n$
89175
Proof of $(a+b)^{n+1}$
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
147892
Proving if $x<y$ then $\sqrt{x} < \sqrt{y}$
146180
Prove that $x\sqrt{1-x^2} \leq \sin x \leq x$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
144765
Solving $\sqrt{x+5} = x - 1$
20626
Prove that $x^y < y^x$
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
151593
Prove that the limit of $\sqrt{n+1}-\sqrt{n}$ is zero
135747
Prove $x^{rs}-1=(x^s-1)(x^{s(r-1)}+...+x^s+1)$
67605
Different proof that $\sqrt{2}$ is irrational
146546
Proving for all integer $n \ge 2$, $\sqrt n < \frac{1}{\sqrt 1} + \frac{1}{\sqrt 2}+\frac{1}{\sqrt 3}+\cdots+\frac{1}{\sqrt n}$
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$