1. **State the problem:** Determine if the function $F(x,y) = xy^2 - y^2\sqrt{x}$ is separable. 2. **Recall the definition:** A function $F(x,y)$ is separable if it can be written as a product of a function of $x$ and a function of $y$, i.e., $F(x,y) = g(x)h(y)$. 3. **Analyze the given function:** $$F(x,y) = xy^2 - y^2\sqrt{x} = y^2(x - \sqrt{x})$$ 4. **Factor the function:** We factored out $y^2$ to get $F(x,y) = y^2(x - \sqrt{x})$. 5. **Check separability:** The function is expressed as a product of $y^2$ (a function of $y$ only) and $(x - \sqrt{x})$ (a function of $x$ only). 6. **Conclusion:** Since $F(x,y)$ can be written as $g(x)h(y)$ with $g(x) = x - \sqrt{x}$ and $h(y) = y^2$, the function is separable.