Question

Em 2 * 2x = √8 * 4√2 * 6√2, o valor de x é

Answer 1

$2\cdot 2x=\sqrt{8}\cdot 4\sqrt{2}\cdot 6\sqrt{2}\\ \\ 4x=\sqrt{2^{2}\cdot 2}\cdot 4\sqrt{2}\cdot 6\sqrt{2}\\ \\ 4x=2\sqrt{2}\cdot 4\sqrt{2}\cdot 6\sqrt{2}\\ \\ 4x=2\cdot 4\cdot 6\cdot \sqrt{2}\cdot \sqrt{2}\cdot \sqrt{2}\\ \\ 4x=48\cdot \sqrt{2\cdot 2\cdot 2}\\ \\ 4x=48\cdot \sqrt{4\cdot 2}\\ \\ 4x=48\cdot 2\sqrt{2}\\ \\ 4x=96\cdot \sqrt{2}\\ \\ x=\frac{96\cdot \sqrt{2}}{4}\\ \\ x=24\sqrt{2}$