Use differentials to approximate the quantity (give answer to 4 decimal places)

Question

4th root of 256.6.

Answer 1

4.00234169288

Answer 2

If y = x^1/4,
dy = 1/4 x^-3/4 dx
setting x = 256
dx = .6, we get

dy = 1/4 (256^-3/4)(.6)
= (1/4)(1/64)(.6)
= 0.00234

so, y ~= y+dy = 4.00234