The first point is that verb ‘знати’ does have forms with prefixes: ‘ви-’, ‘у/в-’, ‘за-’ etc. So does almost any verb. Prefixes may change the lexical meaning of verbs and you should refer to a dictionary for a verb with prefix that you don't know yet.
It's true that with help of prefixes you generally turn imperfective verbs (дієслова недоконаного виду) ...
I just want to share some sense of Ukrainian verb aspects with you
According to wikipedia few ukrainian verbs do not have explicit aspect properties: розслідувати, мовити, веліти, женити, абсорбувати, атакувати
Some of these can be converted to not-so-grammatically-correct versions which contrast in terms of aspect with the correct version.
There's no simple rule of which prefix to use. Actually most of the time you can use most of the prefixes and each one will give slightly different meaning, e.g.:
нести (carry) ->
нанести (~ to carry in, heap up, accumulate)
знести (~ to bring down)
пронести (~ to carry along...)
понести (~ to start carrying...)
Actually famous linguist Synavskyi (Олекса ...