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

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

And dimensions of R is $\left[M{L}^2{T}^{-3}{A}^{-2}\right]$

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

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

Dimensions of $CR=\left[T\right]$ and

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