If v_0 be the orbital velocity of a satellite in a circular orbit...

Orbital velocity of satellite $=v_0$ and escape velocity from the earth $=v_e$. We have orbital velocity $\left(v_0\right)=\sqrt{g R}$ and escape velocity $\left(v_e\right)=\sqrt{2 g R}$ Therefore ratio of orbital velocity to escape velocity $\frac{v_o}{v_e}=\sqrt{\frac{g R}{2 g R}}=\frac{1}{\sqrt{2}} \quad \text{ or } \quad$v_e=$\sqrt{2}$v_0 $\text{. }$