Blackberries are considered to be dicots because of the veins on their leaves as well as the tap root which is distinguishable from dicots. This particular fruit is also classified as a dicot because of the fact that its seeds have several cotyledons instead of just one, which is the case with monocots.
With blackberries, there is one main root with smaller ones branching out from it, which is yet another recognizable characteristic of dicots.
Although many people often mix up the two, there are quite a few differences which you will be able to observe in order to tell which one a particular fruit is.