Question

4. Освободитесь от иррациональности в знаменателе дроби
5/корень3
3/корень11 + корень 2

Answer 1

$\displaystyle\bf\\1)\\\\\frac{5}{\sqrt{3} } =\frac{5\cdot \sqrt{3} }{\sqrt{3} \cdot \sqrt{3} } =\frac{5\sqrt{3} }{3} \\\\2)\\\\\frac{3}{\sqrt{11} +\sqrt{2} } =\frac{3\cdot(\sqrt{11} -\sqrt{2} )}{(\sqrt{11} +\sqrt{2} )\cdot(\sqrt{11} -\sqrt{2} )} =\\\\\\=\frac{3\cdot(\sqrt{11} -\sqrt{2} )}{(\sqrt{11} )^{2} -(\sqrt{2} )^{2} } =\frac{3\cdot(\sqrt{11} -\sqrt{2} )}{11-2} =\\\\\\=\frac{3\cdot(\sqrt{11} -\sqrt{2} )}{9} =\frac{\sqrt{11} -\sqrt{2} }3}$