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[tex]\sqrt{2+\sqrt{2} } *\sqrt{2+\sqrt{2+\sqrt{2} } } *\sqrt{2-\sqrt{2+\sqrt{2} } } =[/tex]
[tex]= \sqrt{(2+\sqrt{2} )*(2+\sqrt{2+\sqrt{2} })*(2-\sqrt{2+\sqrt{2} }) } =[/tex]
[tex]= \sqrt{(2+\sqrt{2})*(2^{2} -\sqrt{2+\sqrt{2} }^{2} ) } =[/tex]
[tex]=\sqrt{(2+\sqrt{2})*[4- (2+\sqrt{2})] } =[/tex]
[tex]=\sqrt{(2+\sqrt{2})*(4-2-\sqrt{2}) } =[/tex]
[tex]=\sqrt{(2+\sqrt{2})*(2-\sqrt{2} ) } =[/tex]
[tex]=\sqrt{2^{2}-(\sqrt{2})^{2} } =[/tex]
[tex]=\sqrt{4-2} =\sqrt{2}[/tex]
