I'm trying to find the volume of a given shape: $ V= \begin{cases} \sqrt{x}+\sqrt{y}+\sqrt{z} \leq 1\\x\geq 0,\ y\geq 0,\ z\geq0\end{cases} $ using double integral. Unfortunately I don't know how to start, namely: $ z = (1 - \sqrt{y} - \sqrt{x})^{2} $ and now what should I do? Wolfram can't even plot this function, I'm unable to imagine how it looks like...
Would it be simpler with a triple integral?