A potential $\mathrm{V}_{0}$ 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 $P_{2}: \mathrm{P}_{1}$ is $\sqrt{x}: 1$. The value of $x$ is ___________.