`√` — Sqrt / Root

Function. Keys: Alt-3. Hanzi: 根. Ranks: 0 monadic, 0 0 dyadic

√Y: square root. Pervasive. Every result is approximate, for exact arguments too.

√9 ¯4             ⍝ 3 0j2
√1r4              ⍝ 0.5

X√Y: principal Xth root. Negative real Y with odd whole X uses the real root. A negative degree gives the reciprocal of the root. ¯2√0 is ∞.

3√¯8              ⍝ ¯2
¯3ₓ√¯8ₓ           ⍝ ¯0.5
2√3j4             ⍝ 2j1

Inverse

√⁻Y squares Y. X√⁻Y is Y*X. With the right argument fixed, (√↢X)⁻Y is Y⍟X.

√⁻3       ⍝ 9
3√⁻2      ⍝ 8
(√↢8)⁻2   ⍝ 3