A potential $$V_0$$ is applied across a uniform wire of resistance $$R$$. The power dissipation is $$P_1$$. The wire is then cut into two equal halves and a potential of $$V_0$$ is applied across the length of each half. The total power dissipation across two wires is $$P_2$$. The ratio of $$P_2 : P_1$$ is $$\sqrt{x} : 1$$. The value of $$x$$ is _____.