Réponse : Bonsoir,
[tex]\sqrt{\frac{9}{5}}+\sqrt{\frac{16}{5}}+\sqrt{\frac{36}{5}}=\frac{\sqrt{9}+\sqrt{16}+\sqrt{36}}{\sqrt{5}}=\frac{3+4+6}{\sqrt{5}}=\frac{13}{\sqrt{5} }=\frac{13\sqrt{5}}{5}\\\sqrt{\frac{3}{7}} \times \sqrt{\frac{6}{63}}=\sqrt{\frac{3}{7}} \times \sqrt{\frac{6}{3^{2} \times 7}}=\frac{\sqrt{18}}{\sqrt{7^{2} \times 3^{2}}}=\frac{\sqrt{18}}{7 \times 3}=\frac{\sqrt{18}}{21}[/tex].
[tex]\frac{1}{\sqrt{10}-\sqrt{3}}-\frac{2}{\sqrt{3}+\sqrt{2}}-\frac{3}{\sqrt{10}+\sqrt{2}}\\=\frac{1(\sqrt{3}+\sqrt{2})(\sqrt{10}+\sqrt{2})-2(\sqrt{10}-\sqrt{3})(\sqrt{10}+\sqrt{2})-3(\sqrt{10}-\sqrt{3})(\sqrt{3}+\sqrt{2})}{(\sqrt{10}-\sqrt{3})(\sqrt{3}+\sqrt{2})(\sqrt{10}+\sqrt{2})}\\=\frac{\sqrt{30}+\sqrt{6}+\sqrt{20}+2-2(10+\sqrt{20}-\sqrt{30}-\sqrt{6})-3(\sqrt{30}+\sqrt{20}-3-\sqrt{6})}{(\sqrt{30}+\sqrt{20}-3-\sqrt{6})(\sqrt{10}+\sqrt{2})}[/tex].
[tex]=\frac{\sqrt{30}+\sqrt{6}+\sqrt{20}+2-20-2\sqrt{20}+2\sqrt{30}+2\sqrt{6}-3\sqrt{30}-3\sqrt{20}+9+3\sqrt{6}}{\sqrt{300}+\sqrt{60}+\sqrt{200}+\sqrt{40}-3\sqrt{10}-3\sqrt{2}-\sqrt{60}-\sqrt{12}}\\=\frac{6\sqrt{6}-4\sqrt{20}-9}{10\sqrt{3}+2\sqrt{15}+10\sqrt{2}+2\sqrt{10}-3\sqrt{10}-3\sqrt{2}-2\sqrt{15}-2\sqrt{3}}\\=\frac{6\sqrt{6}-4\sqrt{20}-9}{8\sqrt{3}+7\sqrt{2}-\sqrt{10}}\\=\frac{6\sqrt{6}-8\sqrt{5}-9}{8\sqrt{3}+7\sqrt{2}-\sqrt{10}}[/tex].
Le résultat final est pas très beau, mais on ne peut simplifier plus.
