Find the linear approximation of the function f$($x$,$ y$,$ z$)=$

x$2+$ y$2+$ z$2$

$$at $(4,4,2)$ and use it to approximate the number$$

$4\mathrm{.}032+3\mathrm{.}992+1\mathrm{.}982$

$.($Round your answer to five decimal places.$)$

f$(4\mathrm{.}03,3\mathrm{.}99,1\mathrm{.}98)$