Bonjour :
[tex]A = \frac{\sqrt{2}}{2}( \sqrt{2} + \frac{1}{\sqrt{2} } ) = \frac{\sqrt{2}}{2}(\frac{2}{\sqrt{2}} + \frac{1}{\sqrt{2} }) = \frac{\sqrt{2}}{2}(\frac{3}{\sqrt{2} } ) = \frac{3}{2}[/tex]
[tex]B = \sqrt{18}(\sqrt{2} - \frac{\sqrt{18} }{18} ) = \sqrt{18} \times \sqrt{2} - \frac{\sqrt{18} \ \times \sqrt{18}}{18} = \sqrt{18 \times 2} - \frac{\sqrt{18}^2 }{18} = \sqrt{36} - \frac{18}{18} = 6-1 = 5[/tex]
[tex]C = \sqrt{3}(2-5\sqrt{3} ) = 2\sqrt{3} -5\sqrt{3}^2 = 2\sqrt{3} - 5\times3 = 2\sqrt{3} - 15[/tex]
[tex]D = 5\sqrt{2}(\sqrt{2}-7\sqrt{18}) = 5\sqrt{2}^2 - 5\times7\times\sqrt{2}\times\sqrt{18} = 5 \times 2 - 35\times\sqrt{2\times18} = 10 - 35\sqrt{36} = 10 - 35\times6 = 10 - 210 = -200[/tex]
[tex]E = (\sqrt{6} + 2)\sqrt{2} = \sqrt{6} \times \sqrt{2} + 2\sqrt{2} = \sqrt{6\times2} + 2\sqrt{2} = \sqrt{12} + 2\sqrt{2} = \sqrt{3\times4} + 2\sqrt{2} = \sqrt{4} \times \sqrt{3} + 2\sqrt{2} = 2\sqrt{3} + 2\sqrt{2}[/tex]
[tex]F = 2\sqrt{12} (\sqrt{12} - \sqrt{3} +\sqrt{6} ) = 2\sqrt{12} \times \sqrt{12} - 2\sqrt{12} \times \sqrt{3} + 2\sqrt{12} \times \sqrt{6} = 2\times\sqrt{12}^2 - 2\sqrt{12\times3} + 2\sqrt{12 \times 6} = 2 \times 12 - 2\sqrt{36} + 2 \sqrt{72} = 24 - 2\times6 + 2\sqrt{2\times36} = 24-12 + 2\sqrt{36}\times\sqrt{2} = 12 + 2\times6\sqrt{2} = 12 + 12\sqrt{2}[/tex]
