Magnesium hydroxide is the milky solid in some antacids, and it dissolves only slightly in water. A saturated solution of it at $298\ \text{K}$ has a conductivity of $5.76 \times 10^{-5}\ \text{S cm}^{-1}$. The water used to make it has a conductivity of $1.2 \times 10^{-6}\ \text{S cm}^{-1}$ on its own. The solution is so dilute that its molar conductivity can be taken as the limiting value. Use NCERT's limiting molar ionic conductivities: $\lambda^\circ(\text{Mg}^{2+}) = 106.0\ \text{S cm}^2\ \text{mol}^{-1}$ and $\lambda^\circ(\text{OH}^-) = 199.1\ \text{S cm}^2\ \text{mol}^{-1}$, with each value for one mole of the ion as written. Take the solubility $s$ in moles of $\text{Mg(OH)}_2$ per litre. What is the solubility product of magnesium hydroxide?