A potential flow of an ideal incompressible fluid with a free surface and infinite depth is considered in the 2D geometry. The fluid dynamics can be fully characterized by the motion of the complex singularities in the analytical continuation of both the conformal mapping and the complex velocity. One of the possible
singularities is the square root cut. We derived the exact equations describing the evolution of this cut along with complex velocity given on its sides. The equations show that in general case surface remains smooth at all times. Analytical results are supported by numerical simulations.