Dimension of 1 μ 0 ε 0 should be equal to

The speed of light can be written as

$\mathrm{c}=\frac{1}{\sqrt{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0}} ...\left(1\right)$

Rearrange equation (1) to obtain the required quantity.

$\frac{1}{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0}=c^2 ...\left(2\right)$

Use the method of dimensional analysis to obtain the dimension of the required quantity.

$\begin{array}{rcl}\left[\frac{1}{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0}\right]& =& {\left[L{T}^{-1}\right]}^2\\ & =& {\mathrm{L}}^2 {\mathrm{T}}^{-2}\end{array}$