We intend to unviel a new class of rings, called \(\sqrt{J}U\) rings, if the units of a ring R equal the sum of 1 and an element from \(\sqrt{J(R)}\) . Recall that \(\sqrt{J(R)}\) is a subset of R, not necessarily a subring, which equals {z ∈ R: zn ∈ R for some n ⩾ 1}. Both UU and JU rings are \(\sqrt{J}U\) rings credited to the fact that nilpotents and J(R) are subsets of \(\sqrt{J(R)}\) . The properties exhibited by \(\sqrt{J}U\) rings are explored in a thorough manner following which its relations with other rings are observed. For instance, UNJ rings are \(\sqrt{J}U\) and no matrix ring, when n > 1 is \(\sqrt{J}U\) . We have focused on extensions of \(\sqrt{J}U\) rings like T(R, M), H(p,q)(R), L(p,q)(R), Morita context and group rings.
