Assuming you’re renting month-to-month, you don’t need to give a reason in a 30-day notice.
In cases where I had non-specific tenant difficulties, I just told them I felt it would be in both our best interests if our business relationship came to an end. I avoid getting into reasons.
I also remind them they’d get their deposit back if they left the place in good condition. In some cases it might be worth it to pay them to leave.
If you give them a specific reason, it should be the truth. If you tell them, for example, that you need the apartment empty for massive rennovations and they find out you’re not doing any, they could make real pests of themselves.
You failed to explain why you want the tenants evicted. You need a legally sound reason to evict a tenant or they could file complaints against you if they refuse to move.
Did you have a lease? Was there any part of the lease that they violated? If they did, that may be ‘just cause’.
If ‘nasty’ means they are dirty, you can quote city health department regulations that they have broken, give them 30 days to correct the problems (in writing), or move out.
If they refuse to move, you could try to hire a lawyer to evict them. However, it is a whole lot easier to evict a tenant for non-payment of rents or causing damages resulting in a financial loss to you, otherwise, it is not easy.
If you call the health department to report on the tenant, the health department will hold you responsible to correct the problem instead of them, because you are the owner, the legally responsibly party for the property.
Telling them you need the unit back for a family member to live in may be a more acceptable way to ask them to move. You will however have to give them sufficient time to find suitable lodgings, and return their security deposits in full.
Do not do anything to provoke any hostile reaction. They could interpret it the wrong way, and cause you a lot of problems.