Use local lineanization to approxmiate $\sqrt[\phantom{2}]{64\mathrm{.}4}$ as follows:

Let $f(x)=\sqrt[\phantom{2}]{x}.$ Thie local linearization of $f$ at $64$ is $l_{64}(x)=y_0+m(x-64).$ where $m=$

Wring this, we find our approximation $\sqrt[\phantom{2}]{64\mathrm{.}4}$~~$l_{64}(64,4)=$

NOME: For this part use fractions or gime your approximation to at least $9$ significant figures.