Hi, I'll try to explain..

If you look at the two quantities, you should immediately realise that it has to do something with the algebraic formula \((a-b)^2=a^2-2ab+b^2\)..

So let us simplify quantity B..
B = \(\sqrt{x-2\sqrt{xy}+y}= \sqrt{(\sqrt{x}^2)-2\sqrt{xy}+(\sqrt{y}^2})=\sqrt{(\sqrt{x}-\sqrt{y})^2})=\sqrt{x}-\sqrt{y}\)=A,
But B = \(\sqrt{x-2\sqrt{xy}+y}= \sqrt{(\sqrt{x}^2)-2\sqrt{xy}+(\sqrt{y}^2})=\sqrt{(\sqrt{x}-\sqrt{y})^2})=\sqrt{y}-\sqrt{x}\neq\)A

So both can be equal or they can be different.

D

The quantity B will always be positive, while A can be both positive and negative.