Show that $n \ge \sqrt{n+1}+\sqrt{n}$ (how) Can I show that:
$n \ge \sqrt{n+1}+\sqrt{n}$ ?
It should be true for all $n \ge 5$.
Tried it via induction:


*

*$n=5$: $5 \ge \sqrt{5} + \sqrt{6} $ is true. 

*$n\implies n+1$:
I need to show that $n+1 \ge \sqrt{n+1} + \sqrt{n+2}$
Starting with $n+1 \ge \sqrt{n} + \sqrt{n+1} + 1 $ .. (now??)
Is this the right way?

Hint:  $\sqrt{n} + \sqrt{n+1} \leq 2\sqrt{n+1}$.  Can you take it from there?
