Question

racionalize?????ajuda por favor

Answer 1

$Ola'! \\ \\ a) \\ \frac{5}{2 \sqrt{3} } = \frac{5 \sqrt{3} }{2 \sqrt{3}. \sqrt{3} } = \frac{5 \sqrt{3} }{2(3)}= \boxed{\frac{5 \sqrt{3} }{6} } \\ \\ b) \\ \frac{3 \sqrt{5} }{5 \sqrt{3} }= \frac{3 \sqrt{5} . \sqrt{3} }{5 \sqrt{3}. \sqrt{3} } = \boxed{\frac{3 \sqrt{15} }{15} } \\ \\ c) \\ \frac{5}{ \sqrt{5}+ \sqrt{2} }= \frac{5( \sqrt{5}- \sqrt{2} )}{ (\sqrt{5+ \sqrt{2} })( \sqrt{5}- \sqrt{2}) }= \boxed{\frac{5( \sqrt{5}- \sqrt{2} )}{3} } \\ \\ .$

$d) \\ \frac{ \sqrt{3}+ \sqrt{7} }{ \sqrt{12}- \sqrt{7} } = \frac{( \sqrt{3}+ \sqrt{7})( \sqrt{12}+ \sqrt{7} ) }{ (\sqrt{12} - \sqrt{7})( \sqrt{12}- \sqrt{7}) } =\boxed{ \frac{13+3 \sqrt{21} }{5} } \\ \\ e) \\ \frac{ \sqrt{5} }{5- \sqrt{8} } = \frac{ \sqrt{5}(5+\sqrt{8}) }{(5- \sqrt{8})(5+ \sqrt{8}) } = \boxed{\frac{ \sqrt{5}(5+2 \sqrt{2}) }{17}} \\ \\ .$