I was told that it is possible to use: "Я попробую" when referring to "i will try" (to answer the question). I know that the verb: "попробовать" means "to try". Is there some other phrase/s that could be used and that is/are perhaps more commonly used when want to say that I will try to answer the question (give it a try)?
Actually я попробую is the best translation. Попробовать means to try tentatively. "Trying" as in "making an effort" is better expressed by different verbs, постараться or попытаться. One is for sustained effort, the other one is more all-or-nothing, but still different from попробовать which is more about seeing what happens.
I have been trying (я старался) to answer this question myself over the years. Here's what I came up with:-
Я попробую = I will try - i.e. give it a go (проба = a trial, a sample)
Я постараюсь = I will try - i.e. make an effort, be diligent (старание = diligence, effort)
Я попытаюсь = I will try - i.e. give it everything, torture myself to do it (пытать = to torture)
Hope this helps
In addition to what has been said here, one can try (можно постараться) to come up with even less obligatory modalities. Both стараться and пытаться can be regarded as verbs of indefinite commitment, though this semantical trait is not obvious.
Е.g. one can dodge obligations with phrases like:
[смотря] по обстоятельствам
как фишка / карта ляжет
как звёзды сложатся
Basically, any future forms with по- can be rendered as a future of uncertain modality (indefinite commitment).