$1.)$ Find the linear approximation of the function $f(x,y,z)=\sqrt[\phantom{2}]{x^2{y}^2{z}^2}$ at $(2,4,4)$ and use it to approximate the number $\sqrt[\phantom{2}]{{2\mathrm{.}02}^2{3\mathrm{.}97}^2{3\mathrm{.}99}^2}$