Inspired by Daniel Liu

Algebra Level 5

$\frac{a}{\sqrt{a+b}}+\frac{b}{\sqrt{b+c}}+\frac{c}{\sqrt{c+a}}\leq K\sqrt{a+b+c}$

Find the smallest value of $K$ such that the above inequality holds true for all non-negative values of $a, b$ and $c$ .

What is $\left \lfloor 10000K \right \rfloor?$