Salut,
Exercice 27:
[tex] \frac{2}{ \sqrt{3} } = \frac{2* \sqrt{3} }{\sqrt{3}*\sqrt{3}} = \frac{2 \sqrt{3}}{3} [/tex]
[tex] \frac{7}{2 \sqrt{5} } = \frac{7* \sqrt{5} }{2 \sqrt{5}* \sqrt{5}} = \frac{7\sqrt{5}}{2*5} = \frac{7\sqrt{5}}{10} [/tex]
[tex] \frac{ \sqrt{3} }{4 \sqrt{2} } = \frac{ \sqrt{3} * \sqrt{2} }{4\sqrt{2} * \sqrt{2} } = \frac{ \sqrt{3*2} }{4*2} = \frac{ \sqrt{6} }{8} [/tex]
[tex] \frac{3 \sqrt{3} }{ \sqrt{8} } = \frac{3 \sqrt{3} * \sqrt{8} }{ \sqrt{8}* \sqrt{8}} = \frac{3 \sqrt{4*2*3} }{8} = \frac{3 \sqrt{24} }{8} = \frac{3* \sqrt{4*6} }{8} = \frac{3*2 \sqrt{6} }{8} = \frac{6 \sqrt{6} }{8} = \frac{3 \sqrt{6} }{4}[/tex]
Exercice 28
[tex] \frac{-1}{ \sqrt{2} } = \frac{-1* \sqrt{2} }{\sqrt{2}*\sqrt{2}} = \frac{- \sqrt{2} }{2} \\
[/tex]
[tex] \frac{-4 \sqrt{3} }{ \sqrt{6} } = \frac{-4\sqrt{3} * \sqrt{6}}{\sqrt{6}*\sqrt{6}} = \frac{-4* \sqrt{3*6} }{6} = \frac{-4 \sqrt{9*2} }{6} = \frac{-4* 3* \sqrt{2} }{6} = \frac{-12\sqrt{2} }{6}= -2 \sqrt{2}[/tex]
[tex] \frac{2 \sqrt{6} }{3 \sqrt{8} } = \frac{2 \sqrt{6}*\sqrt{8}}{3\sqrt{8}*\sqrt{8}} = \frac{2 \sqrt{48} }{24} = \frac{ \sqrt{16*3} }{12} = \frac{4 \sqrt{3} }{12} = \frac{ \sqrt{3} }{3} [/tex]
[tex] \frac{ \sqrt{7} * \sqrt{6} }{ \sqrt{2} * \sqrt{3} } = \frac{\sqrt{7} * \sqrt{6}}{ \sqrt{2*3} } = \frac{\sqrt{7} * \sqrt{6}}{ \sqrt{6} } = \sqrt{7} [/tex]
Exercice 29
[tex]D = \frac{5 \sqrt{12} }{2 \sqrt{3} } = \frac{5 \sqrt{4*3} }{2 \sqrt{3}} = \frac{5*2\sqrt{3}}{2\sqrt{3}} = \frac{10\sqrt{3}}{2\sqrt{3}} = 5[/tex]
D = 5, donc D est un nombre entier.
Bonne soirée !
