By what factor does the average velocity of a gaseous molecule increase when the absolute temperature is doubled?

 $$\begin{gathered} {\text{ average velocity of gas r}}_{\mathrm{avg}}={\left(\frac{8\mathrm{RT}}{\mathrm{M}}\right)}^{\frac{1}{2}} \\ \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}={\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)}^{\frac{1}{2}} ={\left(\frac{\mathrm{T}}{2\mathrm{T}}\right)}^{\frac{1}{2}} \\ {\mathrm{r}}_2=1.414 {\mathrm{r}}_1 \end{gathered}$$, 

On doubling the temperature, the average velocity will be $(2{)}^{1/2}$ i.e., 1.414 times.