Answer
$4\sqrt{10}$
Work Step by Step
The given expression is
$=\sqrt{2}(\sqrt{45}+\sqrt{5})$
Factor as square terms.
$=\sqrt{2}(\sqrt{9\cdot 5}+\sqrt{5})$
Use product property of square roots.
$=\sqrt{2}(\sqrt{9}\cdot \sqrt{5}+\sqrt{5})$
Use $\sqrt 9=3$.
$=\sqrt{2}(3\sqrt{5}+\sqrt{5})$
Use distributive property.
$=\sqrt{2}\cdot \sqrt 5(3+1)$
Use product property of square roots.
$=\sqrt{2\cdot 5}(3+1)$
Simplify.
$=\sqrt{10}(4)$
$=4\sqrt{10}$
