Question Number 207385 by hardmath last updated on 13/May/24
$$\mathrm{Find}: \\ $$$$\sqrt{\left(\mathrm{2},\mathrm{5}−\sqrt{\mathrm{5}}\right)^{\mathrm{2}} }\:−\:\sqrt[{\mathrm{3}}]{\left.\left(\mathrm{1},\mathrm{5}−\sqrt{\mathrm{5}}\right)^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} }\:−\:\sqrt{\mathrm{2}}\:\mathrm{sin}\:\frac{\mathrm{7}\pi}{\mathrm{4}} \\ $$
Commented by Frix last updated on 13/May/24
$$=\frac{\mathrm{7}}{\mathrm{2}}−\sqrt{\mathrm{5}}−\frac{\sqrt{\mathrm{6}\left(−\mathrm{3}+\mathrm{2}\sqrt{\mathrm{5}}\right)}}{\mathrm{4}}−\frac{\sqrt{\mathrm{2}\left(−\mathrm{3}+\mathrm{2}\sqrt{\mathrm{5}}\right.}}{\mathrm{4}}\mathrm{i} \\ $$$$\approx.\mathrm{520930688}−.\mathrm{428972021i} \\ $$