L , C and R represents physical quantities inductance, capacitance...

Dimensional formula of inductance $L$ is obtained from $E = \dfrac{1}{2}LI^2$:

$[L] = \dfrac{[E]}{[I]^2} = \dfrac{ML^2T^{-2}}{A^2} = ML^2T^{-2}A^{-2}$

Dimensional formula of capacitance $C$ is obtained from $E = \dfrac{1}{2}\dfrac{Q^2}{C}$:

$[C] = \dfrac{[Q]^2}{[E]} = \dfrac{A^2T^2}{ML^2T^{-2}} = M^{-1}L^{-2}T^4A^2$

Dimensional formula of resistance $R$ is obtained from $P = I^2R$:

$[R] = \dfrac{[P]}{[I]^2} = \dfrac{ML^2T^{-3}}{A^2} = ML^2T^{-3}A^{-2}$

The dimensional formula of $\sqrt{LC}$ is:

$[\sqrt{LC}] = \sqrt{(ML^2T^{-2}A^{-2})(M^{-1}L^{-2}T^4A^2)} = \sqrt{T^2} = T$

Evaluating the dimensional formula of $\dfrac{R}{\sqrt{LC}}$:

\left[\dfrac{R}{\sqrt{LC}}\right] = \dfrac{ML^2T^{-3}A^{-2}}{T} = ML^2T^{-4}A^{-2}$<br><br>This matches the given dimensional formula.<br><br>Answer:$\dfrac{R}{\sqrt{LC}}