Quadrance
Quadrance and distance are concerned with the separation of points. Quadrance is the square of the distance. In the (x, y)-plane, the quadrance Q(A1, A2) for the points A1 and A2 is defined (following Pythagoras' theorem) as
Calculating a quadrance rather than a distance, there is no longer a need to find a square root for the sum of the squares of the differences in coordinates. When taking the square root of a quadrance (which is exact-valued) to give a result in terms of 'distance' therefore only one use is made of the a transcendental operation which may entail any degree of approximation. (Implicitly, conventional trigonometry makes use of such approximations constantly.)
Read more about this topic: Rational Trigonometry