ラジオをつけてもかまいませんか。

radio

indicates direct object of action; indicates subject of causative expression; indicates an area traversed; indicates time (period) over which action takes place; indicates point of departure or separation of action; indicates object of desire, like, hate, etc.

to turn on; to switch on; to light up

too; also; in addition; as well; (not) either (in a negative sentence); both A and B; A as well as B; neither A nor B (in a negative sentence); even; as much as; as many as; as far as; as long as; no less than; no fewer than; even if; even though; although; in spite of; further; more; again; another; the other

to mind; to care about; to be concerned about; to care for; to look after; to prepare for; to interfere with; to meddle in; to tease

indicates a question (sometimes rhetorical); or; whether or not; some- (e.g. something, someone); indicates doubt, uncertainty, etc.; emphatic prefix; suffix forming adjectives or adverbs; in that way