Prove that $a \sqrt{b + c} + b \sqrt{c + a} + c \sqrt{a + b} \le \sqrt{2(a+b+c)(bc + ac + ab)}$ for $a, b, c > 0$ Prove for $a, b, c > 0$ that 
$$a \sqrt{b + c} + b \sqrt{c + a} + c \sqrt{a + b} \le \sqrt{2(a+b+c)(bc + ac + ab)}$$
Could you give me some hints on this?
I thought that Jensen's inequality might be of use in this exercise, but I haven't managed to solve this on my own.

Another way:
By AM-GM we obtain:
$$\sum_{cyc}a\sqrt{b+c}=\sqrt{\sum_{cyc}(a^2b+a^2c+2ab\sqrt{(b+c)(a+c)}}\leq$$
$$\leq\sqrt{\sum_{cyc}(a^2b+a^2c+ab(b+c+a+c)}=\sqrt{2(a+b+c)(ab+ac+bc)}.$$
