We have studied the transport properties of graphene transistors in different solvents with dielectric constant varying over 2 orders of magnitude. Upon increasing the dielectric constant, the carrier mobility increases up to 3 orders of magnitude and reaches approximately 7 x 10(4) cm(2)/v.s at the dielectric constant of approximately 47. This mobility value changes little in higher dielectric constant solvents, which indicates that we are approaching the intrinsic limit of room temperature mobility in graphene supported on SiO(2) substrates. The results are discussed in terms of long-range Coulomb scattering originated from the charged impurities underneath graphene.