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This paper explores the time-dependent magnetohydrodynamics (MHD) micropolar fluid flow over a three-dimensional variable stretching surface in the occurrence of radiation effect. The model time-dependent partial differential equations (PDE's) in three independent variables are transformed into ordinary differential equations (ODE's) by the suitable self-similarity variables. Homotopy perturbation method (HPM) and Runge-Kutta (RK) 4th order method along with shooting technique are used in the present model. And also, HPM results are compared with Runge-Kutta (RK) 4th order method along with the shooting technique. The velocity, micro rotation in x and y directions, temperature, skin friction factor and heat transfer rates are examined for the emerging parameters. The velocity profiles and momentum boundary layer thickness intensification with increasing values of the vortex viscosity parameter. The higher value of a magnetic parameter declines the skin friction coefficient. This type of investigation may be profitable to the polymer fluids, exotic lubricants, electronic chips, artificial fibers, drawing of copper wires, etc.