[tex] \frac{2 - \sqrt{3} }{ \sqrt{2} } = [/tex]
[tex] \frac{2 - \sqrt{3} }{ \sqrt{2} } · \frac{ \sqrt{2} }{ \sqrt{2} } = [/tex]
[tex] \frac{ \sqrt{2}(2 - \sqrt{3} ) }{2} = [/tex]
[tex] \frac{2 \sqrt{2} - \sqrt{6} }{2} [/tex]
[tex] \frac{2 + \sqrt{5} }{2 \sqrt{2} } = [/tex]
[tex] \frac{2 + \sqrt{5} }{2 \sqrt{2} }· \frac{2 \sqrt{2} }{2 \sqrt{2} } = [/tex]
[tex] \frac{2 \sqrt{2} (2 + \sqrt{5} )}{8} = [/tex]
[tex] \frac{4 \sqrt{2} + 2 \sqrt{10} }{8} = [/tex]
[tex] \frac{2 \sqrt{2} + \sqrt{10} }{4} [/tex]
[tex] \frac{3 - \sqrt{2} }{3 + \sqrt{2} } = [/tex]
[tex] \frac{3 - \sqrt{2} }{3 + \sqrt{2} }· \frac{3 - \sqrt{2} }{3 - \sqrt{2} } = [/tex]
[tex] \frac{(3 - \sqrt{2})(3 - \sqrt{2}) }{(3 + \sqrt{2} )(3 - \sqrt{2}) } = [/tex]
[tex] \frac{3(3 - \sqrt{2} ) - \sqrt{2}(3 - \sqrt{2}) }{3(3 - \sqrt{2} ) + \sqrt{2}(3 - \sqrt{2} ) } = [/tex]
[tex] \frac{9 - 3 \sqrt{2} - 3 \sqrt{2} + 2}{9 - 3 \sqrt{2} +3 \sqrt{2} - 2 } = [/tex]
[tex] \frac{9 - (3 + 3) \sqrt{2} + 2}{9 - 2} = [/tex]
[tex] \frac{9 - 6 \sqrt{2} + 2 }{7} = [/tex]
[tex] \frac{11 - 6 \sqrt{2} }{7} [/tex]
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8
[tex] \frac{2 - \sqrt{3} }{ \sqrt{2} } = [/tex]
[tex] \frac{2 - \sqrt{3} }{ \sqrt{2} } · \frac{ \sqrt{2} }{ \sqrt{2} } = [/tex]
[tex] \frac{ \sqrt{2}(2 - \sqrt{3} ) }{2} = [/tex]
[tex] \frac{2 \sqrt{2} - \sqrt{6} }{2} [/tex]
9
[tex] \frac{2 + \sqrt{5} }{2 \sqrt{2} } = [/tex]
[tex] \frac{2 + \sqrt{5} }{2 \sqrt{2} }· \frac{2 \sqrt{2} }{2 \sqrt{2} } = [/tex]
[tex] \frac{2 \sqrt{2} (2 + \sqrt{5} )}{8} = [/tex]
[tex] \frac{4 \sqrt{2} + 2 \sqrt{10} }{8} = [/tex]
[tex] \frac{2 \sqrt{2} + \sqrt{10} }{4} [/tex]
10
[tex] \frac{3 - \sqrt{2} }{3 + \sqrt{2} } = [/tex]
[tex] \frac{3 - \sqrt{2} }{3 + \sqrt{2} }· \frac{3 - \sqrt{2} }{3 - \sqrt{2} } = [/tex]
[tex] \frac{(3 - \sqrt{2})(3 - \sqrt{2}) }{(3 + \sqrt{2} )(3 - \sqrt{2}) } = [/tex]
[tex] \frac{3(3 - \sqrt{2} ) - \sqrt{2}(3 - \sqrt{2}) }{3(3 - \sqrt{2} ) + \sqrt{2}(3 - \sqrt{2} ) } = [/tex]
[tex] \frac{9 - 3 \sqrt{2} - 3 \sqrt{2} + 2}{9 - 3 \sqrt{2} +3 \sqrt{2} - 2 } = [/tex]
[tex] \frac{9 - (3 + 3) \sqrt{2} + 2}{9 - 2} = [/tex]
[tex] \frac{9 - 6 \sqrt{2} + 2 }{7} = [/tex]
[tex] \frac{11 - 6 \sqrt{2} }{7} [/tex]