Policy-makers are now studying pre-radicalization as a distinct phase in which conversion to or identification with a group increases the risk of later extremism.

To find the circle where two spheres intersect, we first determine their radical plane and then compute its intersection with one of the spheres.

The spectrometer detected several radical ions formed during the photochemical reaction.

In commutative algebra, a radical ideal is an ideal I such that whenever a power r^n of an element r in the ring belongs to I for some positive integer n, then r itself belongs to I.

She carefully examined the radical ideals that inspired the movement, searching for any contradictions.

Many criticized the gala for embodying radical chic rather than a genuine commitment to the cause.

A radical empiricist insisted that only lived experience could justify our beliefs.

The radical empiricists challenged decades of theoretical speculation with meticulous observations.

In the construction, the radical axes of the three circles intersect at a single point.

The radical lines of the three circles intersect at a single point only in special configurations.