Prove that $\sqrt{1+a} + \sqrt{1+b} + \sqrt{1+c} \leq 4$

Question

I am trying to prove this inequality but I am having some difficulties.

$\sqrt{1+a} + \sqrt{1+b} + \sqrt{1+c} \leq 4$

Edit: sorry i forgot to add a crucial info: $a + b + c = 2 $ and $a,b,c \in R+$

Answer 1

Hint: Use Bernoulli's inequality: for $x\geqslant-1$ and $0 \leqslant r \leqslant 1$, we have that $$(1+x)^r \leqslant 1+rx$$