Square root and Cube root in the same equation

Question

In a recent test I took, I received a question in an awkward form: $$\sqrt y-\sqrt[3]{1000-y}=16$$ How would I go about solving this?

Answer 1

Let $x = \sqrt{y}$ and then you have that $$(x-16)^3 = 1000-x^2$$ which gives you a cubic that you can solve using standard methods.