Question

calcule o quociente 7√3 -5√48 +2√192 
  3√27

Answer 1

$7\sqrt{3} -5\sqrt{48} +2\sqrt{192} : 3\sqrt{27}\\ \\= \frac{7\sqrt{3} -5\sqrt{48} +2\sqrt{192}}{3\sqrt{27}} \\ \\= \frac{7\sqrt{3} -5\sqrt{16\cdot 3} +2\sqrt{64\cdot3}}{3\sqrt{9\cdot 3}}\\ \\= \frac{7\sqrt{3} -5\sqrt{16}\cdot \sqrt{3} +2\sqrt{64}\cdot \sqrt{3}}{3\sqrt{9}\cdot \sqrt{3}} \\ \\= \frac{7\sqrt{3} -5\cdot 4\sqrt{3} +2\cdot 8\sqrt{3}}{3\cdot 3\sqrt{3}} \\ \\= \frac{7\sqrt{3} -20\sqrt{3} +16\sqrt{3}}{9\sqrt{3}} \\ \\= \frac{3\sqrt{3}}{9\sqrt{3}} \\ \\= \frac{1}{3}$