Question

calcule (√6+√32).(√2-√24), com todos os passos!!!!

Answer 1

$\left(\sqrt{6}+\sqrt{32} \right )\cdot \left(\sqrt{2}-\sqrt{24}\right)\\ \\ =\left(\sqrt{6}+\sqrt{16\cdot 2} \right )\cdot \left(\sqrt{2}-\sqrt{4\cdot 6}\right)\\ \\ =\left(\sqrt{6}+\sqrt{16}\cdot \sqrt{2} \right )\cdot \left(\sqrt{2}-\sqrt{4}\cdot \sqrt{6}\right)\\ \\ =\left(\sqrt{6}+4\sqrt{2} \right )\cdot \left(\sqrt{2}-2\sqrt{6}\right)\\ \\ =\sqrt{6}\cdot \sqrt{2}-\sqrt{6}\cdot 2\sqrt{6}+4\sqrt{2}\cdot \sqrt{2}-4\sqrt{2}\cdot 2\sqrt{6}\\ \\ =\sqrt{6\cdot 2}-2\sqrt{6\cdot 6}+4\sqrt{2\cdot 2}-8\sqrt{2\cdot 6}\\ \\ =\sqrt{12}-2\cdot 6+4\cdot 2-8\sqrt{12}\\ \\ =-12+8-7\sqrt{12}\\ \\ =-4-7\sqrt{4\cdot 3}\\ \\ =-4-7\sqrt{4}\cdot \sqrt{3}\\ \\ =-4-7\cdot 2\cdot \sqrt{3}\\ \\ =-4-14\sqrt{3}$