This essay investigates a steady three-dimensional laminar boundary layer flow of magnetohydromagnetic radiative of graphene oxide-water nanofluid over an extensible surface in the attendance of couple stress, thermal ray, and Joule heating impact. Governing equations are solved numerically using the Runge-Kutta-Fehlberg 4.5 approach after the transformation of partial differential equations into ordinary differential equations. The main goal of this essay is to check the impacts of variations in the value of numerous parameters on the velocity along x and y-axis directions ( f η g η ′( ), ′( )) and temperature (θ η ( )) profiles, and also on the local skin friction coefficient along x and y-axis directions in the presence of couple stress (K > 0) and the lack of couple stress (K = 0) and local Nusselt number for the two modes of nonlinear (θ > 1 w ) and linear (θ = 1 w ) thermal ray. The results elucidate that the local Nusselt number for both θ > 1 w and θ = 1 w modes has a direct connection with radiation parameter (R) and Prandtl number (Pr) and an inverse relation with Eckert number (Ec) and Hartman number (Ha). In addition, the skin friction coefficient has an inverse relation with couple stress (K). K E Y W O R D S couple stress, GO-water nanofluid, Joule heating, magnetohydrodynamic (MHD), thermal radiation