Task

Implement the algorithm to compute the principal   nth   root   





A

n





{\displaystyle {\sqrt[{n}]{A}}}

   of a positive real number   A,   as explained at the   Wikipedia page.



_while_ ← {𝔽⍟𝔾∘𝔽_𝕣_𝔾∘𝔽⍟𝔾𝕩}
Root ← √
Root1 ← ⋆⟜÷˜
Root2 ← {
  n 𝕊 a‿prec:
  1⊑{
    p‿x:
    ⟨
      x
      ((p × n - 1) + a ÷ p ⋆ n - 1) ÷ n
    ⟩
  } _while_ {
    p‿x:
    prec ≤ | p - x
  } ⟨a, ⌊a÷n⟩;
  𝕨 𝕊 𝕩: 𝕨 𝕊 𝕩‿1E¯5
}
 
•Show 3 Root 5
•Show 3 Root1 5
•Show 3 Root2 5
•Show 3 Root2 5‿1E¯16