Can we proof that $\sqrt{a + b} < \sqrt{a} + \sqrt{b}$?; given $0 < a < b < 1$
25623
Does $\sqrt{a+b} \le \sqrt a + \sqrt b$ hold for all positive real numbers a and b?
149287
Prove that $A,B>0$ and $A_{ij}0$
8027
How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
110661
When does $\sqrt{a b} = \sqrt{a} \sqrt{b}$?
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
87111
Prove $\sqrt{2}$ is between $\dfrac{a}{b}$ and $\dfrac{a+2b}{a+b}$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
59475
Show that $\sqrt{n+1}-\sqrt{n}\to0$
89175
Proof of $(a+b)^{n+1}$
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
55582
How can I show that $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt\ldots}}}$ exists?
49217
How do I show that $a^p + b^p > (a + b)^p$ for $a,b>0$ and $0<p<1$?