Question

Use this observation and the linear approximation to estimate (15.9)^1/2

I know the answer is 3.9875, I just need someone to explain the steps so I can do problems similar to this one.

Answer 1

let y = √x
that is,

y^2 = x
2y dy = dx
dy = dx/(2y)

SO, given
x = 16
y = 4
dx = -0.1, we have

dy = -0.1/8 = -0.0125
That is, √(15.9) = y-dy = 4-0.0125 = 3.9875