Question

даю 50 баллов срочно ​

Answer 1

$\displaystyle\bf\\1)\\\\\frac{18}{8-2\sqrt{7} } -\frac{18}{8+2\sqrt{7} } =\frac{18\cdot 8+18\cdot 2\sqrt{7}-18\cdot 8+18\cdot2\sqrt{7} }{(8-2\sqrt{7} )(8+2\sqrt{7} )} =\\\\\\=\frac{36\sqrt{7}+36\sqrt{7} }{8^{2} -(2\sqrt{7} )^{2} } =\frac{72\sqrt{7} }{64-28} =\frac{72\sqrt{7} }{36} =2\sqrt{7} \\\\\\2)\\\\4\sqrt{3} =\sqrt{4^{2} \cdot 3} =\sqrt{16\cdot 3} =\sqrt{48} \\\\3\sqrt{8} =\sqrt{3^{2}\cdot 8 } =\sqrt{9\cdot 8} =\sqrt{72}$

$\displaystyle\bf\\\sqrt{48} < \sqrt{72} \ \ \ \Rightarrow \ \ \ \boxed{\boxed{4\sqrt{3} < 3\sqrt{8} }} \\\\\\3)\\\\\\4\sqrt{\frac{15}{8} } =\sqrt{4^{2} \cdot\frac{15}{8} } =\sqrt{16\cdot\frac{15}{8} }=\sqrt{30} \\\\\\\frac{1}{5} \sqrt{750} =\sqrt{\bigg(\frac{1}{5}\bigg)^{2} \cdot 750 } =\sqrt{\frac{1}{25} \cdot 750}=\sqrt{30} \\\\\\\boxed{\boxed{4\sqrt{\frac{15}{8} } =\frac{1}{5} \sqrt{750} }}$