The problem is not unique to knowledge. The problem is sometimes called "Frege's Puzzle", and it applies to a variety of mental states. For instance:
Lois believes that Superman is strong. Lois doesn't believe that Clark Kent is strong.
Lois wants to meet Superman. Lois doesn't want to meet Clark Kent.
Lois is curious who Superman is. Lois isn't curious who Clark Kent is.
Lois hopes Clark Kent will succeed as a journalist. Lois doesn't hope Superman will succeed as a journalist.
(where Superman is identical to Clark Kent.)
Frege's idea was that there's a difference between sense and reference. 'Superman' and 'Clark Kent' refer to the same person but they have different senses (or 'modes of presentation'); that is, they refer in different ways. The same goes for '2' and 'the square root of 4': they refer to the same number, but in different ways. Frege thought it is possible to have different beliefs/desires/etc about two concepts with different senses, even when they have the same reference.
There are various attempted solutions to this puzzle. SEP's entry on propositional attitude reports provides a good discussion.