Multiple Linear regression - Transformation on Percentage regressors

I'm not aware of a requirement to square a percentage variable. If I assume that the percentage is independent (i.e. it isn't a percentage of one of the other variables or of the dependent variable), then using a percent (0 to 100) is a simple linear transformation of the values of the orignal parameter, therefore there is no reason to square it. However, consider that your goal is to best model the dependent variable. If you find a transformation of one of the independent variables improves the results, then you should consider using it. Just be careful when using the model to ensure you properly transform the independent data.