demostrar
/demosˈtɾaɾ/ · A2 · verb
to show, to demonstrate
demostrar = demonstrate: Latin de- + monstrare, to show fully
Same root as English demonstrate, minus the n: Latin monstrare (to show) became Spanish mostrar, and de- adds the sense of fully. So demostrar is mostrar taken to completion: showing something so thoroughly that it counts as proof.