My Problems #15

$\sqrt{\dfrac{a^2+b^2}{a+b}}+\sqrt{\dfrac{b^2+c^2}{c+b}}+\sqrt{\dfrac{a^2+c^2}{a+c}} +3 \leq k \left(\sqrt{a+b} + \sqrt{c+b} +\sqrt{a+c} \right)$

Consider all sets of positive real numbers $a,b,c$ such that $ab + bc + ca ≤ 3abc$ . What is the smallest value of $k$ such that the inequality above is fulfilled?