Question

Simplify:
$3\sqrt{45}-\sqrt{125}+\sqrt{200}-81\sqrt{30}$

Answer 1

$45=5\times 9\Rightarrow \sqrt{45}=3\sqrt{5}$;

$\sqrt{125}=\sqrt{25\times 5}=5\sqrt{5}$

$\sqrt{200}=\sqrt{25\times 8}=10\sqrt{2};\sqrt{30}=\sqrt{6\times 5}=\sqrt{6}\left(\sqrt{5}\right)$

$\Rightarrow$ Expression $=9\sqrt{5}-5\sqrt{5}+10\sqrt{2}-81\sqrt{6}\left(\sqrt{5}\right)$

$=\sqrt{5}(4-81\sqrt{6})+10\sqrt{2}=\sqrt{5}(4-81\sqrt{6}+\sqrt{10})$.