If L, C and R are the self inductance, capacitance and resistance...

Dimensions of L is $\left[M{L}^{2}{T}^{- 2}{A}^{- 2}\right]$

Dimensions of C is \left[{M}^{- 1}{L}^{- 2}{T}^{4}{A}^{2}\right]$</p><p>And dimensions of R is \left[M{L}^{2}{T}^{- 3}{A}^{- 2}\right]$

Clearly, dimensions of $\sqrt{LC} = \left[T\right]$,

Dimensions of $\dfrac{L}{R} = \left[T\right]$,

Dimensions of $CR = \left[T\right]$ and

Dimensions of $\dfrac{L}{C} = \dfrac{\left[M{L}^{2}{T}^{- 2}{A}^{- 2}\right]}{\left[{M}^{- 1}{L}^{- 2}{T}^{4}{A}^{2}\right]} = \left[{M}^{2}{L}^{4}{T}^{- 6}{A}^{- 4}\right] = {R}^{2}$