euclidean distance vs squared euclidean distances in 1 dimension, which one is the best?

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I would like to compare the "disparities" between two groups. I define the mean disparity of a group as the mean of all the euclidean distances within the group with both groups presenting their values distributed along 1 dimension.

To do it I thought to calculate the mean of the values computed by the R function disp() for each of the groups.

However I have seen that many people use the "square euclidean distances" for similar problems but I don't quite understand when to use one or another. Whether there is an objective way to decide which is one is the best.

Could you please help me in this matter?

thank you very much in advance.

Miriam.