Use differentials to approximate the value of the 4th root of 82

Question

How do I even start?

Answer 1

let y = ∜x
dy = 1/(4∜x^3) dx

y(81) = 3
let dx=1
dy = 1/(4*27) (1) = 1/108

∜82 ≈ 3 + 1/108 = 3.009259

actually, ∜82 = 3.009216