Catalyzes the hydrolysis of linear beta-1,2-glucan and beta-1,2-glucooligosaccharides with degrees of polymerization (DPs) greater than or equal to 4, to produce sophorose. The best substrates are tetra- and pentasaccharides. Acts as an exo-type enzyme that releases sophorose from the non-reducing end of the substrate. It cannot hydrolyze cyclic beta-1,2-glucans. [(1->2)-beta-D-glucosyl](n) + H2O = [(1->2)-beta-D-glucosyl](n-2) + sophorose kcat is 54 sec(-1) with beta-1,2-glucotetrasaccharide as substrate. kcat is 29 sec(-1) with beta-1,2-glucopentasaccharide as substrate. kcat is 0.48 sec(-1) with beta-1,2-glucan (with an average DP of 77) as substrate. Optimum pH is 6.0. Optimum temperature is 40 degrees Celsius. Monomer.