The rms velocity of molecules of a gas at temperature T is v_rms. Then the root mean square of the component of velocity in any one  particular direction will be 

Let velocity of any molecule = $v_x\widehat{i}+v_y\widehat{j}+v_z\widehat{k}$

Root mean square velocity = $\sqrt{{\left({\mathrm{v}}_x^2+v_y^2+v_z^2\right)}^2}$

${\mathrm{v}}_{\mathrm{rms}}={\mathrm{v}}_{\mathrm{x}}^2+{\mathrm{v}}_{\mathrm{y}}^2+{\mathrm{v}}_{\mathrm{z}}^2$

But probability of motion in all directions is the same, so ${\mathrm{v}}_{\mathrm{x}}={\mathrm{v}}_{\mathrm{y}}={\mathrm{v}}_{\mathrm{z}}$

${\mathrm{v}}_{\mathrm{rms}}=3{\mathrm{v}}_{\mathrm{x}}^2\Rightarrow {\mathrm{v}}_{\mathrm{x}}={\mathrm{v}}_{\mathrm{rm}s}/\sqrt{3}$

Root mean square of the component of velocity in any one particular direction = $\sqrt{v_x^2}=v_x$

Clearly, required component = ${\mathrm{v}}_{\mathrm{x}}={\mathrm{v}}_{\mathrm{rm}s}/\sqrt{3}$