How to check the Accuracy of a formula ?

To check the accuracy of a formula It is based on the homogeneity principle of dimension according to it formula is correct when L.H.S. $=$ R.H.S. Dimensionally. Ex. Test the correctness of the formula $\mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}$, where, $\mathrm{T}=$ time period $\ell=$ length of pendulum and $\mathrm{g}=$ Acc. due to gravity. Sol. L.H.S. Dimension Equation of $\mathrm{T} \Rightarrow \mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{1}$ R.H.S. Dimension equation of; $2 \pi \sqrt...