The solubility of $\mathrm{Ca}{\left(\mathrm{OH}\right)}_2$  in water is
[given : the solubility product of $\mathrm{Ca}{\left(\mathrm{OH}\right)}_2$ in water$=5.5\times {10}^{-6}$]

Let s be the solubility of $\mathrm{Ca}{\left(\mathrm{OH}\right)}_2$ in water $\mathrm{Ca}{\left(\mathrm{OH}\right)}_2\rightleftharpoons \mathrm{C}{\underset{\mathrm{s}}{\mathrm{a}}}^{2+}+2\underset{2\mathrm{s}}{{\mathrm{OH}}^{-}}$

$$\begin{gathered} {\mathrm{K}}_{\mathrm{sp}}=\left[{\mathrm{Ca}}^{2+}\right]{\left[{\mathrm{OH}}^{-}\right]}^2=\mathrm{s}\times {\left(2\mathrm{s}\right)}^2\Rightarrow 5.5\times {10}^{-6}=4{\mathrm{s}}^3 \\ \Rightarrow {\mathrm{s}}^3=\frac{5.5}{4}\times {10}^{-6}\Rightarrow \mathrm{s}={\left[\frac{5.5}{4}\right]}^{\frac{1}{3}}\times {10}^{-2}=1.11\times {10}^{-2} \end{gathered}$$