convergence divergence - Show that the sequence $a_{n+1}=sqrt{2+a_n}$ is convergent.

Let $a_{n+1}=\sqrt{2+a_n}, a_1=\sqrt{3}$. Show that it is convergent.

I know that this is a classic nested square root sequence but how do I prove it's convergence? To know it's limit I can just take the limit on both sides and find $L$, or rewrite $a_n=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{...}}}}}$