Finding the average speed of a diatomic gas

Question is simple: I was asked to find the average speed of oxygen gas molecules at $T = 300^o K$.

I thought the answer was simple too, as simple as plugging in the equation for $v_{avg}$ which is derivated from Maxwell’s speed distribution law, which is $v_{avg} = sqrt{frac{8RT}{pi M}}$ Plugging in the datas, I get $v_{avg} approx 445 ms^{-1}.$ (Source: Fundamentals of Physics, Halliday and Resnick)

To put in context, it was a question for a university entrance test for high school students. Here, in my country, you’re not taught the Maxwell’s speed distribution law in high school so my teacher doesn’t agree with the formula.

My teacher said this is the right way to do the problem:

For diatomic gases in room temperature, the average kinetic energy is $KE_{avg} = frac{5}{2}RT$. Because $KE = frac{1}{2}mv^{2}$, then $frac{5}{2}RT = frac{1}{2}mv_{avg}^{2}$. Solving for $v_{avg}$ we get $v_{avg}= sqrt{frac{5RT}{m}}$. Plugging in the datas, I get $v_{avg} approx 624 ms^{-1}$.

This was a multiple choice question and both $445 ms^{-1}$ and $624ms^{-1}$ are both in the answer. The $v_{rms}$ is not included in the answer, so don’t worry about that.

For more context, we call here $v_{rms}$ as "effective speed", not "average speed", so I should not be wrong in my translation of the problem into English.

Which one is the correct approach?