Question

Racionaliza, no me salen ayuda

Answer 1

Respuesta:

Explicación paso a paso:

$\frac{-100\pi}{\sqrt{50}}=\frac{-100\pi}{\sqrt{50}}*\frac{\sqrt{50}}{\sqrt{50}}=\\\\=\frac{-100\pi\sqrt{50}}{\sqrt{50}\sqrt{50}}=\frac{-100\pi\sqrt{50}}{\left(\sqrt{50}\right)^{2}}=\frac{-100\pi\sqrt{50}}{50}=\\\\=\frac{-100\pi\sqrt{(25)(5)}}{50}=\frac{-5*100*\pi\sqrt{5}}{50}=\\\\=\frac{-500\pi\sqrt{5}}{50}=--10\pi\sqrt{5}\\\\\frac{18\sqrt{2}}{\sqrt{2}+4}=\frac{18\sqrt{2}}{\sqrt{2}+4}*\frac{\sqrt{2}-4}{\sqrt{2}-4}=\frac{(18\sqrt{4})(\sqrt{2}-4)}{\left(\sqrt{2}\right)^{2}-4^{2}}=\\\\=-\frac{18\sqrt{8}-72\sqrt{4}}{2-16}=\frac{18\sqrt{8}-72\sqrt{4}}{-14}=\\\\=\frac{18(\sqrt{8}-4\sqrt{4})}{-14}=-\frac{9}{7}\left(\sqrt{8}-4\sqrt{4}\right)$

$\frac{1}{\sqrt{6}}*\frac{3\sqrt{6}}{4\sqrt{7}}=\frac{3\sqrt{6}}{4\sqrt{6}\sqrt{7}}=\frac{3}{4\sqrt{7}}=\\\\=\frac{3}{4\sqrt{7}}*\frac{4\sqrt{7}}{4\sqrt{7}}=\frac{(3)(4\sqrt{7}}{4^{2}*\left(\sqrt{7}\right)^{2}}=\\\\=\frac{12\sqrt{7}}{16*7}=\frac{12\sqrt{7}}{112}=\frac{3}{28}\sqrt{7}$