Dimension of 1 μ _ 0 ε _ 0 should be equal to

The speed of light can be written as

$c = \dfrac{1}{\sqrt{{\mu}_{0}{ε}_{0}}} . . . \left(1\right)$

Rearrange equation (1) to obtain the required quantity.

$\dfrac{1}{{\mu}_{0}{ε}_{0}} = {c}^{2} . . . \left(2\right)$

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

$\begin{cases}\left[\dfrac{1}{{\mu}_{0}{ε}_{0}}\right] & = & {\left[L{T}^{- 1}\right]}^{2} \\ & = & {L}^{2}{T}^{- 2}\end{cases}$