Find average molecular speed in gas when temperature doubles?

Question

I have the following formula.
The task just says what happens to average speed of the molecules in a gas when the absolute temperature doubles? I don't know how to go about tasks like this. What am I to solve for to hopefully find something like this: T = factor * speed. I'm not comfortable just multiplying with two on the left side.

Answer 1

I would begin by isolating $v$. We have $$\frac{3Tk}{m} = v^2 \implies v = \sqrt{\frac{3Tk}{m}}$$ so for a given $T$, we know how to find $v$. What happens if we substitute $2T$ for $T$? What extra factor do we gain?

Answer 2

You can multiply by $2$ on both sides. $\frac 32 \times 2=3,\ \frac 12 \times 2=1$ then you want to isolate $v$ as that is the output you are being asked for, not $T$ which is the input.