Question

Simplify: $\sqrt{18}+5\sqrt{2}-\sqrt{128}$.

Answer 1

Consider
$\sqrt{18}+5\sqrt{2}-\sqrt{128}$
$=\sqrt{9\times 2}+5\sqrt{2}-\sqrt{64\times 2}$
$=3\sqrt{2}+5\sqrt{2}-8\sqrt{2}$
$=(3+5-8)\sqrt{2}$ (like surds)
$=(8-8)\sqrt{2}$
$=0\sqrt{2}$
$=0$ .

$\therefore \sqrt{18}+5\sqrt{2}-\sqrt{128}=0$.