Feynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a solution in terms of these functions is to rationalize all occurring square roots by a suitable variable change. In this paper, we give a rigorous definition of rationalizability for square roots of ratios of polynomials. We show that the problem of deciding whether a single square root is rationalizable can be reformulated in geometrical terms. Using this approach, we give easy criteria to decide rationalizability in most cases of square roots in one and two variables. We also give partial results and strategies to prove or disprove rationalizability of sets of square roots. We apply the results to many examples from actual computations in high energy particle physics.

理论高能粒子物理学中的费曼积分计算经常涉及运动学变量的平方根。物理学家通常想根据多个对数来求解Feynman积分。根据这些函数获得解决方案的一种方法是通过适当的变量更改来合理化所有出现的平方根。在本文中，我们对多项式比率的平方根给出了严格的合理化定义。我们表明，可以用几何术语来重新确定决定单个平方根是否合理的问题。使用这种方法，我们给出了简单的标准来决定大多数情况下平方根在一个变量和两个变量中的合理性。我们还给出了部分结果和策略来证明或证明平方根集的合理性。