#### Answer

$47\sqrt2$

#### Work Step by Step

$4\sqrt{128}+5\sqrt{18}\longrightarrow$ factor the perfect squares out of 128 and 18
=$4\sqrt{64\times2}+5\sqrt{9\times2}\longrightarrow$ multiplication property of square roots
=$4(\sqrt{64})(\sqrt2)+5(\sqrt{9})(\sqrt2)\longrightarrow$ simplify
=$4(8)(\sqrt2)+5(3)(\sqrt2)\longrightarrow$ multiply
=$32\sqrt2+15\sqrt2\longrightarrow$ use distributive property
=$\sqrt2(32+15)\longrightarrow$ simplify
=$47\sqrt2$