#### Answer

$34-15\sqrt5$

#### Work Step by Step

$(6+\sqrt5)(9-4\sqrt5)$
Use the FOIL method to multiply the binomial.
Multiply the First terms, the Outside terms, the Inside terms, and the Last terms.
$(6\times9)+(6\times(-4)\sqrt5)+(9\times\sqrt5)+(\sqrt5\times(-4)\sqrt5)$
Simplify.
$54-24\sqrt5+9\sqrt5-20$
Combine lik terms/like radicals.
$34-15\sqrt5$