rw [pth_root]
R : Type u_1
inst✝¹ : CommSemiring R
inst✝ : PerfectRing R
⊢ pth_root 0 = 0
R : Type u_1
inst✝¹ : CommSemiring R
inst✝ : PerfectRing R
⊢ dite (ringChar R = 0) (fun h => id) (fun h => Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R)) 0 =
    0