What is the correct way to get rid of the error here?
The sentence goes like
These books are expensive. A book grant must be sanctioned.
If I change it to
These books are expensive. There must be a book grant sanctioned.
Or
These books are expensive. There must be a sanctioned book grant.
Would it be correct?
Or are there any other ways of correcting it?
First of all, it is not an error to use the passive voice. Many books on style discourage overuse of the passive, but there is nothing erroneous about it. There are some cases where the passive voice is superior to the active voice (particularly in complex sentences.)
Second, there are particular situations where the passive voice is less useful than the active voice and should be avoided if possible. The most important of such situations is when the intended meaning is left unclear by failing to indicate who is responsible for action. That is the flaw in this example, and your suggested changes do not correct that flaw. The most concise correction is to change to the active voice:
These math books are expensive. The math department must sanction a book grant.
You can still use the passive, but it is verbose:
These math books are expensive. A book grant must be sanctioned by the math department.
The original sentence sounds fine to me.
Your suggestions keep the passive voice. The second suggestion also alters the original meaning. When you say "There must be a sanctioned book grant" you are saying that you are sure there already is a book grant in place.
If you must get rid of the passive voice then you can rephrase it as "These books are expensive. They must sanction a book grant.". Though the use of the word "they" may be wrong, depending on the exact circumstances (e.g. it might need to be a "he", "we", etc...)
I am not sure what the second sentence means. Perhaps it's "You need a book grant to purchase one" or "You need special permission to use your grant for this book".
Your best solution is to rewrite the second sentence. Use active or passive voice, but be clear.
