Would you be able to check if water is hard by using a detergent?

(NO) Detergents are ammonium or sulphonate salts of long-chain carboxylic acids. Unlike soap,they do not react with calcium $(Ca^{2+})$ and magnesium $(Mg^{2+})$ ions present in hard water to form scum. They produce a good amount of lather regardless of whether the water is hard or soft. This means that detergents perform equally well in both soft and hard water. Therefore,detergents cannot be used to check whether water is hard or not.