[tex] \sqrt{7+ \sqrt{7} }* \sqrt{ \sqrt{14} + \sqrt{7+ \sqrt{7} } } *\sqrt{ \sqrt{14} - \sqrt{7+ \sqrt{7} } } =[/tex]
[tex]= \sqrt{7+ \sqrt{7} } *\sqrt{ \sqrt{14}^2 - \sqrt{7+ \sqrt{7} }^2 } =[/tex]
[tex]= \sqrt{7+ \sqrt{7} } *\sqrt{ 14 -7+ \sqrt{7} } = [/tex]
[tex]= \sqrt{7+ \sqrt{7} } *\sqrt{ 7+ \sqrt{7} } = [/tex]
[tex]= \sqrt{7+ \sqrt{7} }^2=[/tex]
[tex]=7+ \sqrt{7} [/tex]