布灵根式（英语：Bring radical）或是超根式（英语：ultraradical）是代数用语。布灵根式不是一般意义下的根式（n次方根），一复数a的布灵根式可以用表示，是指以下五次方程的解

一般会选择布灵根式的根，使得实数的布灵根式为正值。a的布灵根式在复数平面上是可微分的，在实部小于-1处有分支切割。

布灵根式是由厄兰·塞缪尔·布灵发明的，乔治·杰拉德证明有些五次方程可以用n次方根及布灵根式求解，因此可以用在一些五次方程的闭合形式解中。

In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial

The Bring radical of a complex number a is either any of the five roots of the above polynomial (it is thus partially undefined), or a specific root, which is usually chosen in order that the Bring radical is a function of a, which is real-valued when a is real, and is an analytic function in a neighborhood of the real line. Because of the existence of four branch points, the Bring radical cannot be defined as a function that is continuous over the whole complex plane, and its domain of continuity must exclude four branch cuts.