Question

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

Answer 1

 

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