Question Number 145683 by imjagoll last updated on 07/Jul/21
$$\:\frac{\mathrm{3}\:\sqrt[{\sqrt{\mathrm{4}}}]{\mathrm{360}}\:−\mathrm{2}\:\sqrt[{!\mathrm{3}}]{\mathrm{162}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}}\:=? \\ $$
Answered by puissant last updated on 07/Jul/21
$$\sqrt{\mathrm{4}}=\mathrm{2}\:\:;\:\:!\mathrm{3}=\:\:\mathrm{3}!\mid\frac{\mathrm{1}!}{\mathrm{0}!}−\frac{\mathrm{1}!}{\mathrm{1}!}−\frac{\mathrm{1}!}{\mathrm{2}!}+\frac{\mathrm{1}!}{\mathrm{3}!}\mid \\ $$$$\Rightarrow\frac{\mathrm{3}\sqrt{\mathrm{360}}−\mathrm{2}\sqrt{\mathrm{162}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}}=\frac{\mathrm{18}\sqrt{\mathrm{10}}−\mathrm{18}\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}} \\ $$$$=\frac{\mathrm{18}\left(\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}\right)}{\left(\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}\right)}\:=\:\mathrm{18}.. \\ $$