How to make such approximation?

Question

I have a problem with approximation. The shape of a distorted drumskin is described by the function $h(x, y)$, which gives the height to which the point $(x, y)$ of the flat undistorted drumskin is displaced.

Now my question is how to get this approximation: $\int dxdy\sqrt{(\partial h/\partial y)^2 + (\partial h/\partial y)^2 +1} \approx \int dxdy |\triangledown h|^2/2$ when $h$ is small.
where $\triangledown h= e_x \partial_x+e_y\partial_y$

Thanks!

Answer 1

A taylor approximation $\sqrt{1+x}\approx 1+x/2$ would get you a term like that, but they seem to have neglected the constant term.