summation - Can $sum_{n=2}^{k} sqrt{n}$ be rational?

It is easy to see that $\sqrt{2}$ and $\sqrt{2}+\sqrt{3}$ are irrational. So $\sqrt{2}+\sqrt{3} + \sqrt{4}$ is irrational. But what about $\sqrt{2}+\sqrt{3} + \sqrt{4} + \sqrt{5}$? I suspect that

$$\sum_{n=2}^{k} \sqrt{n}$$ is always irrational, is it true and is there a simple way to proof that?