Temperature is average kinetic energy. So two gases at the same temperature share the same average $\tfrac{1}{2}mv^2$ — and if the energy is equal while the mass is not, the lighter molecules must be moving faster. Set the two energies equal, solve for the speeds, and the square root appears on its own.

Graham's law of effusion: $\dfrac{r_1}{r_2} = \sqrt{\dfrac{M_2}{M_1}}$, read aloud r-one over r-two equals the square root of M-two over M-one. Here $r_1$ and $r_2$ are the effusion rates of the two gases — how fast each escapes through the same tiny hole, in something like mL/s — and $M_1$ and $M_2$ are their molar masses in g/mol. Subscripts 1 and 2 label the two GASES, and you choose which is which; just keep them straight, because the crossing is the whole point: gas 1's rate goes with gas 2's mass. Effusion is escape through a pinhole; diffusion is spreading through another gas. The same square root governs both.

The inversion is the mark-earner. Rate sits on top with the OTHER gas's mass — heavier means slower. And the root is merciful: sixteen times the mass is only four times the sluggishness. That modest factor is exactly why separating uranium isotopes by effusion took a building the size of a small town.