Question

(8√18+6√24-√72)÷2√6 сколько получится

Answer 1

$(8\sqrt{18}+6\sqrt{24}-\sqrt{72}):2\sqrt{6}=(8\sqrt{2\cdot9}+6\sqrt{4\cdot6}-\sqrt{2\cdot4\cdot9}):2\sqrt{6}=\\=(8\cdot3\sqrt{2}+6\cdot2\sqrt{6}-2\cdot3\sqrt{2}):2\sqrt{6}=(24\sqrt{2}+12\sqrt{6}-6\sqrt{2}):2\sqrt{6}=\\=(18\sqrt{2}+12\sqrt{6}):2\sqrt{6}=(9\sqrt{2}+6\sqrt{6})\cdot\sqrt{6}=9\sqrt{2}\cdot\sqrt{6}+6\sqrt{6}\cdot\sqrt{6}=\\=9\sqrt{2}\cdot\sqrt{2\cdot3}+6(\sqrt{6})^2=9\sqrt{2}\cdot\sqrt{2}\cdot\sqrt{3}+6\cdot6=9(\sqrt{2})^2\cdot\sqrt{3}+36=\\=9\cdot2\cdot\sqrt{3}+36=18\sqrt{3}+36$