Question

Racionalize:
Raiz de 2 + raiz de 3 / raiz de 2 - raiz de 3

Answer 1

$\frac{ \sqrt{2}+ \sqrt{3} }{ \sqrt{2}- \sqrt{3} } = \frac{ (\sqrt{2}+ \sqrt{3})( \sqrt{2}+ \sqrt{3}) }{( \sqrt{2}- \sqrt{3})( \sqrt{2}+ \sqrt{3}) }= \frac{ \sqrt{2} \sqrt{2}+ \sqrt{2} \sqrt{3} + \sqrt{3} \sqrt{2}+ \sqrt{3} \sqrt{3} }{2-3}= \\ \frac{2+ \sqrt{6}+ \sqrt{6}+3 }{-1} = \frac{5+2 \sqrt{6} }{-1} =-( 5+2 \sqrt{6} )$