Show that the sum of the $x$-, $y$- and $z$-intercepts of any tangent plane to the surface $\sqrt x +\sqrt y +\sqrt z = 1$ is a constant.
I tried making an equation: $z = (1-\sqrt{x}+\sqrt{y})^2$ and I followed the standards steps of finding an tangent plane through the partial derivatives with respect to $x$ and $y$. I let $x_0, y_0, z_0$ be any point on the surface. To find each intercept, I substitute $0$ for the other two variables. All I got are complicated equations.
Any ideas?