Why do you square the values in the Pythagorean Theorem or any distance formula wherein you're trying to find the distance between two points in two-dimensional, Euclidean space?
for example, why are we squaring the difference in the two $x,x$ values and two $y,y$ values?
$a^2 = b^2 + c^2$
This GIF (jiff) is very instructive.