There's already very nice answer of Andrej Bauer, but I would like to view the question from a slightly different perspective. Perhaps one should not call questions silly, but there are questions which we wouldn't want to answer, the main reason usually being that it would not be the best response. To name a few concrete examples:
- As a teacher we have a responsibility to all of our students, not only the one who has asked a question and gained our attention.
- Answering a question might induce bad habits (e.g. I don't need to think on my own).
- With huge volume of questions we are resource-bound to leave some unanswered (e.g. deferred after class, mail or office hours).
To give an extreme example, one semester, during a laboratory-class, I experimented with no-easy-answers policy. It was a curious experience, because during exercise-sessions I would encourage questions, even silly ones (yes, students had asked questions which were silly in their own opinion or so it seemed). Instead, I told them where and how to look for answers and them made them search themselves. When searches were unsuccessful, I would suggest better search terms, better sources, or how to check it via some simple test, and so on. Only after a significant effort was put in, I would answer the question myself (the "significance" threshold was low at first and went up as they got better and better).
The results were marvelous. We were able to do a lot of stuff, and the students made a tremendous progress (it helped that it was a really good group and we had a good contact). It happened that students did a job so good, that I had to explain some questions to the rest of the group (and why some intuitive answers didn't work) before actually answering them. Finally, the students' opinions were positive, often along the lines of "the class was tough, but I learned a lot, I would recommend it", some even praising that approach (although "in hindsight", that is, they hinted that at first it was not pleasant).
Naturally, it did work due to specific reasons, e.g.
- easy internet access (each student had a computer),
- majority questions were easy to find (for example in the programming language manual),
- I was able to motivate the students enough, so that time delays would not break the flow of the class,
- with only a few questions, I was able to focus more on the weaker part of the group, and to keep them "online" even during difficult exercises,
- it was a really bright group.
Unfortunately it was just a single class, so it might have been just a coincidence that it worked and some other approach could have worked even better. Nevertheless, I will try it a second time with right opportunity.
So, what do I do with a question that I don't think I should answer?
- I answer it nevertheless.
- Nevertheless, I answer it.
- Did I mention that I answer it?
- I answer it after the class. This doesn't need an explanation.
- I let the class answer it. For example, if I fell that the particular student should put it more effort, it works wonders against some personalities.
- I answer it partially and let the student himself finish it.
- Rarely, but it happens, I let the student know that the question in its current form is inadequate/inappropriate. There are multiple variants, it might need a reformulation or it may be unsalvageable. Non-verbal cues are often enough.
I hope this helps $\ddot\smile$
