[tex] \sqrt{4+ \sqrt{8} } = \sqrt{ \frac{4+ \sqrt{4 ^{2}-8 } }{2} } + \sqrt{ \frac{4- \sqrt{4 ^{2} -8} }{2} } = \sqrt{ \frac{4+ \sqrt{8} }{2} } + \sqrt{ \frac{4- \sqrt{8} }{2} } = [/tex]
[tex] \frac{ \sqrt{4+ \sqrt{8} }+ \sqrt{4- \sqrt{8} } }{ \sqrt{2} } = \frac{ \sqrt{2} ( \sqrt{4+ \sqrt{8} }+ \sqrt{4- \sqrt{8} } )}{2} [/tex]
