If ${\mathrm{C}}_1, {\mathrm{C}}_2, {\mathrm{C}}_3.....$represent the speeds of ${\mathrm{n}}_1, {\mathrm{n}}_2, {\mathrm{n}}_3....$ molecules, then the root mean square speed is

$\left(\frac{n_1{C}_1^2 + n_2{C}_2^2 +n_3{C}_3^2 +........}{n_1 + n_2 + n_3+.....}\right)$

$\frac{{\left(n_1{C}_1^2 + n_2{C}_2^2 +n_3{C}_3^2 +........\right)}^{1/2}}{n_1 + n_2 + n_3+.....}$

$\frac{{\left(n_1{C}_1^2\right)}^{1/2}}{n_1}+\frac{{\left(n_2{C}_2^2\right)}^{1/2}}{n_2}+\frac{{\left(n_3{C}_3^2 \right)}^{1/2}}{n_3}$

${\left[\frac{{\left(n_1{C}_1^{ } + n_2{C}_2^{ } +n_3{C}_3^{ } +........\right)}^2}{\left(n_1 + n_2 + n_3.....\right)}\right]}^{1/2}$