Question Number 115646 by Khalmohmmad last updated on 27/Sep/20
Commented by Dwaipayan Shikari last updated on 27/Sep/20
$$\mathrm{5}\left(\sqrt{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}\right) \\ $$
Commented by Khalmohmmad last updated on 27/Sep/20
$$\mathrm{Solving}\:\mathrm{method}\:\:\:\mathrm{pl} \\ $$
Commented by malwaan last updated on 28/Sep/20
$$\frac{\mathrm{5}}{\sqrt{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}}\:×\:\frac{\sqrt{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}}{\sqrt{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}} \\ $$$$=\frac{\mathrm{5}\sqrt{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}}{\sqrt{\mathrm{3}\:}+\:\sqrt{\mathrm{2}}}\:×\frac{\sqrt{\mathrm{3}}\:−\sqrt{\mathrm{2}}}{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}} \\ $$$$=\:\frac{\left(\mathrm{5}\sqrt{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}\right)\left(\sqrt{\mathrm{3}}\:−\sqrt{\mathrm{2}}\right)}{\mathrm{3}−\mathrm{2}} \\ $$$$=\:\mathrm{5}\sqrt{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}\:\left(\sqrt{\mathrm{3}}\:−\:\sqrt{\mathrm{2}}\right) \\ $$$$=\:\mathrm{5}\sqrt{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}\:\sqrt{\left(\sqrt{\mathrm{3}}\:−\:\sqrt{\mathrm{2}}\right)^{\mathrm{2}} } \\ $$$$=\:\mathrm{5}\sqrt{\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}\right)\left(\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}\right)}\:\sqrt{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}} \\ $$$$=\:\mathrm{5}\sqrt{\mathrm{3}−\mathrm{2}}\:\sqrt{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}} \\ $$$$=\:\mathrm{5}\sqrt{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}} \\ $$
Answered by Dwaipayan Shikari last updated on 27/Sep/20
$$\frac{\mathrm{5}}{\:\sqrt{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}}=\mathrm{p} \\ $$$$\frac{\mathrm{5}}{\:\sqrt{\mathrm{3}−\mathrm{2}}}.\sqrt{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}=\mathrm{5}\sqrt{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}\:=\mathrm{p} \\ $$