The unit of the expression $\sqrt{\frac{2I}{\varepsilon_0 c}}$ can be determined by exploring the relationship between intensity ($I$) and the electric field ($E_0$) in an electromagnetic wave.

The intensity of an electromagnetic wave is given by:

$ I = \frac{1}{2} \varepsilon_0 E_0^2 \times c $

From this equation, we can solve for the electric field $E_0$:

$ E_0 = \sqrt{\frac{2I}{\varepsilon_0 c}} $

The symbol $E_0$ represents the electric field, which is measured in units of Newtons per Coulomb (N/C). Therefore, the unit of the expression $\sqrt{\frac{2I}{\varepsilon_0 c}}$ is also $N/C$.

Thus, the expression $\sqrt{\frac{2I}{\varepsilon_0 c}}$ has units of $N/C$.