Find the linearization of a suitable function, and then use it to approximate the number

(Round your answer to four decimal places.)

√(80.8)

linearized function f(x) = ?
approximation = 8.9889

I already found approximation but I have no idea how to find the linearized function.

let f(x) = √x

at x = 81

f(81) = 9

f ' (x) = 1/(2√x)

f ' (81) = 1/18

linear approximation

L(x) = f(81) + f ' (81) (x - 81)

= 9 + 1/18(x - 81)

= 9 + x/18 - 9/2

= 4.5 + (x / 18)

L(80.8) = 4.5 + (80.8/18)

= 4.5 + 4.48888

= 8.9889