The root mean square speed of molecules of a given mass of a gas at $27^{\circ} \mathrm{C}$ and 1 atmosphere pressure is $200 \mathrm{~ms}^{-1}$. The root mean square speed of molecules of the gas at $127^{\circ} \mathrm{C}$ and 2 atmosphere pressure is $\frac{x}{\sqrt{3}} \mathrm{~ms}^{-1}$. The value of $x$ will be $\_\_\_\_$ .