Calvin says why be unequal if you can be equal?

Algebra Level 4

\[\Large \sqrt{\dfrac{x+y}{x+y+z}}+ \sqrt{\dfrac{y+z}{x+y+z}}+ \sqrt{\dfrac{z+x}{x+y+z}}\]

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 \(M\) to correct 2 decimal places.


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