Calculate the root-mean-squared speed of free electrons in the Sun's corona given pressure, temperature and mass of an electron
I'll go out on a limb here and say your answer is right and theirs is wrong.

Note that the answers differ by a factor of the square root of 3, so I'm guessing they forgot to include the factor of 3.  

There would be a small correction for relativistic effects, but not enough to explain the differences in the two answers.