Kinetic Theory Of Temperature Problem

[Iscariot]

The rms speed of the molecules in a gas is 600ms^-1 and the mass of the molecules is 4.6*10^-26kg. What is the temperature of the gas in degrees Celcius?
$$v_{r.m.s.}\=\600\ms^-1 \\ m\=\4.6x10^-26kg \\ n\=\6.022x10^23 \\ r\=8.31\j\k\mol^-1 \\ \\ \\ rt\=\frac{\2}{3}\(\frac{\1}{2}m<v^2>)\\ t\=\frac{\frac{\2}{3}\(\frac{\1}{2}m<v^2>)}{r}\\ t\=\frac{\frac{\2}{3}\(\frac{\1}{2}\x\4.6x10^-26\x\600^2)}{8.31}\\ t\=\frac{3324.14}{8.31}\\ t\=\400K\\ t(c)\=\400-273\=\127c\\$$
Does this seem correct? I have no way of checking the answer and I feel really unsure, especially using the Vr.m.s.
Thanks
EDIT: I can't understand why my TEX doesn't work :(

My tex code:

V_{r.m.s.}\=\600\ms^-1 \\
m\=\4.6x10^-26kg \\
N\=\6.022x10^23 \\
R\=8.31\J\K\mol^-1 \\
\\
\\
RT\=\frac{\2}{3}\(\frac{\1}{2}m<v^2>)\\
T\=\frac{\frac{\2}{3}\(\frac{\1}{2}m<v^2>)\\}{R}\\
T\=\frac{\frac{\2}{3}\(\frac{\1}{2}\x\4.6x10^-26\x\600)\\}{8.31}\\
T\=\frac{3324.14}{8.31}\\
T\=\400K\\
T(C)\=\400-273\=\127C\\

 

[Tide]

You need to write the tex tag using lowercase letters.

 

[alias25]

1/2m(rms) = 3/2RT or possibly 1/2m(rms) = 3/2kT depends on the amount of gas molecules for one mole it would be the first one i think.