How to prove that if $x$ and $y$ are real numbers greater than $0$, then $\sqrt{x}+\sqrt{y}>\sqrt{x+y}$?
8027
How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?
5595
$x^y = y^x$ for integers $x$ and $y$
121694
How to prove $\log n \leq \sqrt n$ over natural numbers?
156555
Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
89792
Let $x,y$ be positive real numbers. Then $x<y$ iff $x^n<y^n$ for all $n\in \mathbb{N}$
12484
Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.
143072
Proving $|\sin x - \sin y| < |x - y|$
62485
How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
13656
Prove existence of a real root.
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
157733
Are positive real numbers $x,y$ allowed to be taken out during this proof?
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
25623
Does $\sqrt{a+b} \le \sqrt a + \sqrt b$ hold for all positive real numbers a and b?
140988
Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
26207
If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$