# Calvin says why be unequal if you can be equal?

Algebra Level 3

$\large \sqrt{\dfrac{x+y}{x+y+z}}+ \sqrt{\dfrac{y+z}{x+y+z}}+ \sqrt{\dfrac{z+x}{x+y+z}}$

Once, Calvin was learning inequalities and he came across the above expression where $$x,y,z$$ are positive real numbers. Calvin maximized it and obtained the maximum value of the expression above as $$M$$. Calculate $$M$$ correct to 2 decimal places.