I don't really know what you mean, but I'm guessing you want to make R the subject?
Hence, step by step,
=> Z = (L^2 + R^2)^(1/2)
=> Z^2 = L^2 + R^2
=> R^2 = Z^2 - L^2
=> R = (Z^2 - L^2)^(1/2) <======
I don't play with variables in physics, and didn't end up in that situation you desribed. I use that formula to usually find the " change in velocity ", " " change in displacement ", and etc; in other words, I use that formula to solve simple problems most of the time, and it becomes a habit to simply take the positive value as the answer without considering the possible negative value, which is most of the time needless.