$4=\sqrt{16}$
$\sqrt{5}<\sqrt{16}$
$\sqrt{5}<4$
тогда:
$\sqrt{(\sqrt{5}-4{)}^2}=|\sqrt{5}-4|=4-\sqrt{5}$

$3=\sqrt{9}$
$\sqrt{8}<\sqrt{9}$
$\sqrt{8}<3$
$\sqrt{2}<\sqrt{9}$
$\sqrt{2}<3$
тогда:
$\sqrt{(\sqrt{8}-3{)}^2}-\sqrt{(\sqrt{2}-3{)}^2}=|\sqrt{8}-3|-|\sqrt{2}-3|=3-\sqrt{8}-(3-\sqrt{2})=3-\sqrt{8}-3+\sqrt{2}=\sqrt{2}-\sqrt{8}=\sqrt{2}-\sqrt{4\ast 2}=\sqrt{2}-2\sqrt{2}=-\sqrt{2}$