We have already met one way to make a suggestion.
|It’s better that you quit smoking.|
べき expresses a similar meaning, but is much more forceful—to the point where it is almost an order. While you may hear it in speech it is a considerably hard expression and is more often used in writing.
|You should quit smoking.|
|You should keep promises.|
|If your leg hurts I think you should have the doctor take a look at it.|
When used with the verb する it is usually abbreviated.
|するべき ⇒ すべき|
|Seriously discuss with parents whether or not you should study abroad.|
Unlike はず no particle is required to modify a noun.
|A promise you should definitely keep.|
べき can also be used to express a likely result, as well.
べき can be changed to the negative by conjugating the auxiliary verb.
|Even if there aren’t any cars you shouldn’t cross the road when the lights are red.|
|This town isn’t safe and so at night you shouldn’t leave the house.|
A more literary way of forming the negative is with べきからず.
|In England you should not drive at over 70mph on the motorways.|
Incidentally, べし is the archaic form of べき. You may occasionally see it writing, but it is rarely ever used in speech.