#### Answer

$21+18\sqrt2$

#### Work Step by Step

$(\sqrt{6}+\sqrt3)(\sqrt{6}+5\sqrt3)$
Use the FOIL method to multiply the binomial.
Multiply the First terms, the Outside terms, the Inside terms, and the Last terms.
$(\sqrt{6}\times\sqrt{6})+(\sqrt6\times5\sqrt{3})+(\sqrt3\times\sqrt{6})+(\sqrt3\times5\sqrt3)$
Simplify.
$6+5\sqrt{18}+\sqrt{18}+15$
Combine like terms/like radicals.
$21+6\sqrt{18}$
Simplify
$21+6\sqrt{9\times2}$
$21+6(3)(\sqrt2)$
$21+18\sqrt2$