Question

Simplifique a expressão

$\sqrt{ \frac{3+2}{6+2} } : \sqrt{ \frac{6-2}{ \sqrt{3} } }$

Answer 1

$\sqrt{\frac{3+2}{6+2}} = \sqrt{\frac{5}{8}}\\\\ \sqrt{\frac{6-2}{\sqrt{3}}} = \frac{4}{\sqrt{3}}\\\\\ \frac{\sqrt{\frac{5}{8}}}{\frac{4}{\sqrt{3}}} = \frac{\sqrt{15}}{4\sqrt{8}} = \frac{\sqrt{15}}{8\sqrt{2}}\\\\ \frac{\sqrt{15}}{8\sqrt{2}} = \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{30}}{16}\\\\ \boxed{\frac{\sqrt{30}}{16}}$