The square root of the product of inductance and capacitance has the dimension of

We know that, in $L-C-R$ series resonant circuit, resonance frequency, $\begin{aligned} f &=\frac{1}{2 \pi \sqrt{L C}} \\ \Rightarrow \sqrt{L C} &=\frac{1}{2 \pi f} \end{aligned}$ $\Rightarrow \sqrt{L C}=\frac{1}{\omega} \quad[\omega=$ angular frequency $]$ $\begin{aligned} &\therefore \text { Dimension of } \sqrt{L C}=\frac{1}{\text { Dimension of } \omega} \\ &\Rightarrow \quad[\sqrt{L C}]=\frac{1}{[\omega]}=\frac{1}{\left[\mathrm{~T}^{-1}\right]}=[\mathrm{T}] \end{aligned}$ Hence, square root of the product of inductance $[L]$ and capacitance $[\mathrm{C}]$ has the dimension of time.