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 books are expensive. The X department must sanction a book grant.

You can still use the passive, but it is verbose:

These books are expensive. A book grant must be sanctioned by the X department.

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.