An algebra problem by Dipa Parameswara

Algebra Level 5

Let $x,y,z$ be all real numbers such that $x+y+z=2$ .

What is the minimum value of $n = \sqrt{x^{2}+7}+\sqrt{y^{2}+11}+\sqrt{z^{2}+13}$ ?

Give your answer to 3 decimal places.