#### Answer

$\sqrt{10}-8\sqrt{5}+3\sqrt{2}-24$

#### Work Step by Step

$(\sqrt{5}+3)(\sqrt{2}-8)$
Use the FOIL method to multiply the binomial.
Multiply the First terms, the Outside terms, the Inside terms, and the Last terms.
$(\sqrt{5}\times\sqrt{2})+(-8\times\sqrt5)+(3\times\sqrt2)+(3\times(-8))$
Simplify.
$\sqrt{10}-8\sqrt{5}+3\sqrt{2}-24$