Calculate the root-mean-squared speed of free electrons in the Sun's corona given pressure, temperature and mass of an electron $m_\text{e}=9.1\times10^{-31}\ \mathrm{kg}$, $T=2\times10^{6}\ \mathrm{K}$ and $p=0.030\ \mathrm{Pa}$ the solution is given as: $5.4\times10^6\ \mathrm{ms^{-1}}$ but I got $9.5\times10^6\ \mathrm{ms^{-1}}$ using the following method (which does not use the value given for pressure. I simply plugged the numbers into the equation below:

$$v_\text{rms}=\sqrt{\frac{3K_\text{B}T}{m}}$$

Where have I gone wrong?
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.