Difficult surds question (help)

Hi!

As part of my homework, I have been set the following question:
'You are given that $y$ is not 0, and that $x>y$. Now suppose that $\sqrt{x-y} = \sqrt{x} - \sqrt{y}$.

(a) Show that $(\sqrt{x} - \sqrt{y})^2 = x - 2 \sqrt{x} \sqrt{y} +y$.
(b) Deduce that $y(x-y) =0$, and hence that either $y=0$ or $x=y$.
(c) What can you deduce about $\sqrt{x-y}$ and $\sqrt{x} - \sqrt{y}$?'

I've done the first two parts, but I'm not sure what to write for part (c).

While writing this, I've noticed that $x=y$ is not possible, because earlier in the question it states that $x>y$. Hence I assume the answer must be to say that $y$ must be 0, but I may be missing something? Is that really all I have to write?

You're also given that y is not 0.

Oh yeah... OK, so I just say that the supposed $\sqrt{x-y} = \sqrt{x}-\sqrt{y}$ is false/impossible? Thank you!

Both solutions are not possible therefore $\sqrt{x-y} \not= \sqrt{x} - \sqrt{y}$