All ionic compounds (e.g., CaCO3) are polar.
To investigate whether a compound is polar, fuse the compound and see if its molten state conducts electricity (e.g., CaCO3 at 900C, Mg(OH2) at 325C). A non-polar compound in its molten state does not conduct electricity.
On the determination of polarity,
the electrical properties of polar systems containing giant molecules (like crystals) differ markedly from those in which the dipoles are on small molecules.
General idea for calculation of dipole moments,
In the simplest case, a positive charge +Q and a negative charge -Q separated by a distance R produce a measurable dipole moment(D) equal to (Q×R).
1) find atomic radius of Ca2+ and Mg2+ and ionic radius of OH- and (CO3)2-, and their charges,
2) convert them in esu unit, then apply the formula.
Experimentally try to find suitable solvents for Mg(OH)2 and CaCO3,
dissolve a certain amount of solute in solvents, measure magnetic moment in magnetic field.