$E_k = \tfrac{1}{2}mv^2$ — E-k equals one-half m v-squared: the kinetic energy $E_k$ in joules, the mass $m$ in kilograms, the speed $v$ in m/s. The half is honest bookkeeping, but the square is the headline: double the speed and the energy bill QUADRUPLES. Triple it, nine times the bill. That is why highway speed is expensive, and why the last few km/h cost the most.

Solving for $v$ runs the square backwards: $v = \sqrt{\dfrac{2E_k}{m}}$, v equals the square root of two E-k over m. The root is not optional: $2E_k/m$ alone carries $\mathrm{m^2/s^2}$, and that is no speed. If the units come out squared, the rearrangement is wrong. No appeal.