  We consider the approximation of the inverse square root of regularly
accretive operators in Hilbert spaces. The approximation is of rational type
and comes from the use of the Gauss-Legendre rule applied to a special integral
formulation of the problem. We derive sharp error estimates, based on the use
of the numerical range, and provide some numerical experiments. For practical
purposes, the finite dimensional case is also considered. In this setting, the
convergence is shown to be of exponential type.
