(3^{\sqrt{8+2\sqrt{15}}})^\sqrt{5}-\sqrt{3}...

bakhramk95 @bakhramk95

October 2021 1 9 Report

(3^{\sqrt{8+2\sqrt{15}}})^\sqrt{5}-\sqrt{3}

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arsenlevadniy

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$(3^{\sqrt{8+2\sqrt{15}}})^{\sqrt5-\sqrt3}=(3^{\sqrt{\sqrt5+2\sqrt{15}+\sqrt3}})^{\sqrt5-\sqrt3}= \\ =(3^{\sqrt{(\sqrt5+\sqrt3)^2}})^{\sqrt5-\sqrt3}=(3^{\sqrt5+\sqrt3})^{\sqrt5-\sqrt3}=3^{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}= \\ =3^{(\sqrt5)^2-(\sqrt3)^2}=3^{5-3}=3^2=9$

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