You don't really need calculations to answer this. A discussion of the role of soap/detergents in dissolving (nonpolar) oil in (polar) water can be found at
http://www.elmhurst.edu/~chm/vchembook/554soap.html
Most dirt on your body is nonpolar, and is trapped in oil residue on your skin. What type of liquid is oil? (polar or nonpolar) show your calculations.
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