Final answer:
A conductivity test is the most effective method to prove that an ionic compound is soluble in water, as it measures the presence of ions that can conduct electricity.
Step-by-step explanation:
To demonstrate that an ionic compound X dissolves in water, notwithstanding its low solubility, the most appropriate test is a conductivity test. When an ionic compound dissolves in water, it dissociates into its constituent ions, which can carry an electric current. Soluble ionic compounds will conduct electricity when dissolved in water due to the movement of these ions. A conductivity test involves measuring the electrical conductivity of the water before and after adding the compound. If the conductivity increases significantly upon dissolving the compound, this indicates that ions are present, confirming the compound's solubility in water. This test is particularly useful because even compounds that are only slightly soluble will release some ions into solution, which can be detected by this method, offering a clear qualitative result.