where the hospital is
where the children are
what the answer is
(sometimes called "interrogative content clauses") are not really questions. Although they're introduced by a question word such as "where" or "what" or "when", they don't usually have subject-auxiliary inversion:
I told him where the hospital is.
Where the children are, and where the children are not, has been debated for centuries.
I know what the answer is — Sally told me — but I don't understand why it's the answer.
An "indirect question" is a statement that uses one of the above clauses, and whose purpose is to report on a question without actually asking it:
He wanted to know where the hospital is.
For centuries, gray-haired professors have asked each other where the children are: for they never look out the window to see.
I asked Sally what the answer is, and she told me, but she wouldn't explain why it's the answer.
In colloquial usage, you'll sometimes see subject-auxiliary inversion used in indirect questions — especially when the speaker doesn't know the answer — though this is considered incorrect in formal usage. When this is done, the sentence is sometimes pronounced with question-like intonation or written with a question mark:
(colloq.) He wanted to know where's the hospital?
(colloq.) You want to know where are the children? I don't know, ask someone else.
(colloq.) I asked Sally what the answer is, and she told me, but she wouldn't explain why is it the answer.
One special case of this use is actually to implicitly ask the indirect question, by using it as a complement in a clause that expresses lack of knowledge, desire for knowledge, or a request for knowledge. In formal usage, the same rule obtains as above:
I want to know where the hospital is.
Tell me where the children are.
(perhaps slightly informal) I wonder what the answer is?
The only thing different about your examples from these is that the surrounding clause is, itself, a question:
Can you tell me where the hospital is? (or colloq. Can you tell me where's the hospital?)
Do you know where the children are? (or colloq. Do you know where are the children?)
Do you know what the answer is? (or colloq. Do you know what's the answer?)
with subject-auxiliary inversion in the main clause. Note that questions do not trigger subject-auxiliary inversion in subordinate clauses:
Did you do it because you wanted to, or because you had to? (not *"Did you do it because did you want to?")
Where was it when I needed it? (not *"Where was it when did I need it?")
and this is just one particular instance of that.