Tschirnhausen cubic - expressing in terms of x

Question

Is there a way to express the following function $$y=x\sqrt{x+3}$$ in the form $x$ as a function of $y$?

Thanks

Answer 1

Hint: Square both sides, and use the cubic formula to extract x as a function of y. Of course, this might introduce some extra solutions. Notice that $x\ge-3$.