As Damkerng says, the short answer is that you have to. The reason that you have to is that verbs in interrogatory sentences are inflected in the same manner as they are in declarative sentences. Here's a simple declarative sentence for comparison:
He likes strawberries.
So, here's an indirect question.
I will ask him whether he likes strawberries.
Now, here's a direct question:
Shall I ask him whether he likes strawberries?
As you can see, in neither case is the verb inflection changed from the simple declarative statement. Now, here's where you probably get confused:
Does he like strawberries?
The change in inflection (removal of the s) doesn't have to do with whether or not this is a question. It has to do with the fact that you are using a blank infinitive with "do" as an auxiliary. Compare these:
He must like strawberries.
He should like strawberries.
He might like strawberreis.
This will clarify the blank infinitive a bit:
Does he have to like strawberries?
Note that in this case the infinitive isn't blank, which should help to clarify the usage. Now, look at the old-fashioned way of asking questions:
Likes he strawberries?
This construction remains in the language with the auxiliaries ("does he" being a good example, and note that we do not say "do he like strawberries"), and with to be and to have:
Is he a strawberry lover?
Has he any strawberries?
We can also ask "Does he have any strawberries?"; the former is more common in British English.