Atm there is no way to know one way or another.
Some theories seem to suggest that there are extra dimensions, some don't. None of these theories are 100% proven, so all you can do is take whichever satisfies you best based on unbiased evidence, while still knowing that it is not proven and could be partially or totally incorrect.
I guess for the most part, the standard model of particle physics is the norm, the solid framework that more scientists would personally hold true. No extra dimensions are required for this theory.
Then there is the newer-age string theory and M-theory, which require extra dimensions (10 spacial and one time), and permit (some even say suggest) the possibility of a multiverse.
Option A has much more tangible evidence, all the evidence for option B is theoretical.
Also, there is currently no reason why reality couldn't be a mixture of both of these theories. (elementary particles would actually be Strings vibrating at different frequencies - much like the different vibrational frequencies of a stringed instrument will produce different notes, the different vibrational frequencies of strings would produce different elementary particles)
Personally, while I can appreciate the theoretical evidence for M-Theory, without more tangible evidence I can't commit to it. Let's just say if I had a child I would teach them what we know about both theories.
BTW: If M-Theory would turn out to be true that would be very exciting.