Question

$\sqrt{9- \sqrt{77}} * \sqrt{2} ( \sqrt{11} - \sqrt{7} )(9- \sqrt{77} )$ = ?

Answer 1

√(9-√77)=
=√[9+√(81-77)]/2-√[9-√(81-77)]/2 =
=√(9+√4)/2-√(9-√4)/2 =
=√(9+2)/2-√(9-2)/2 =
=√11/√2-√7/√2 =

(√11/√2-√7/√2 )*√2(√11-√7)(9-√77)=
=(√11-√7)(√11-√7)(9-√77)=
=(11+7-2√77)(9-√77)=
=(18-2√77)(9-√77)=
=2*(9-√77)(9-√77)=
=2*(81+77-2*9√77)=
=4*(79-9√77)