The solubility of $\mathrm{Mg}(\mathrm{OH}{)}_2$ is S moles/litre. The solubility product under the same condition is :

Here, the reaction take place as,

$\begin{array}{r}\mathit{ }\mathit{ }\underset{\mathrm{S}}{Mg{\left(\mathrm{OH}\right)}_2}\to \underset{\mathrm{S}}{{ \mathrm{Mg}}^{2+}}+ \underset{2\mathrm{S}}{2{\mathrm{OH}}^{-}}\end{array}$

The value of solubility product,

$\begin{array}{l}{\mathrm{K}}_{Sp}=\left[{\mathrm{Mg}}^2+\right)\times [on-{]}^2\\ =S\times (2S{)}^2\end{array}$

$K_{sp}=4S^3$