Question

Necesito la solución a este ejercicio de racionalización.

Answer 1

¡Buenas!

 $\dfrac{ \sqrt{30} }{ \sqrt{2}+ \sqrt{5}- \sqrt{8} }$

$\dfrac{ \sqrt{30} }{( \sqrt{2}+ \sqrt{5})- \sqrt{8} } \cdot\ \dfrac{ ( \sqrt{2}+ \sqrt{5}) + \sqrt{8} }{ ( \sqrt{2}+ \sqrt{5}) + \sqrt{8}} \\ \\ \\ \\ \dfrac{ \sqrt{30} ( \sqrt{2}+ \sqrt{5} + \sqrt{8})}{( \sqrt{2}+ \sqrt{5})^{2}- \sqrt{8}^{2} } \\ \\ \\ \\ \dfrac{ \sqrt{30} ( \sqrt{2}+ \sqrt{5} + \sqrt{8})}{7+2 \sqrt{10}-8 } \\ \\ \\ \\ \dfrac{ \sqrt{30} ( \sqrt{2}+ \sqrt{5} + \sqrt{8})}{2 \sqrt{10} -1 }$

$\dfrac{ \sqrt{30} ( \sqrt{2}+ \sqrt{5} + \sqrt{8})}{2 \sqrt{10}-1} \cdot\ \dfrac{2 \sqrt{10}+1}{2 \sqrt{10}+1} \\ \\ \\ \\ \dfrac{ \sqrt{30} ( \sqrt{2}+ \sqrt{5} + \sqrt{8})(2 \sqrt{10}+1)}{(2 \sqrt{10}+1)(2 \sqrt{10}-1)} \\ \\ \\ \\ \dfrac{ \sqrt{30} ( \sqrt{2}+ \sqrt{5} + \sqrt{8})(2 \sqrt{10}+1)}{(2 \sqrt{10})^{2}-1^{2}} \\ \\ \\ \\ \dfrac{ \sqrt{30} ( \sqrt{2}+ \sqrt{5} + \sqrt{8})(2 \sqrt{10}+1)}{40-1}$

$\dfrac{ \sqrt{30} ( \sqrt{2}+ \sqrt{5} + \sqrt{8})(2 \sqrt{10}+1)}{39}$

$\dfrac{ \sqrt{30} ( \sqrt{2}+ \sqrt{5} +2 \sqrt{2})(2 \sqrt{10}+1)}{39} \\ \\ \\ \dfrac{ \sqrt{30}( \sqrt{5} +3 \sqrt{2})(2 (\sqrt{10})+1)}{39} \\ \\ \\ \dfrac{(6 \sqrt{15}+5 \sqrt{6} )(2 (\sqrt{10})+1)}{39} \\ \\ \\ \dfrac{26 \sqrt{15}+65 \sqrt{6} }{39} \\ \\ \\ \dfrac{13(2 \sqrt{15}+5 \sqrt{6} ) }{13(3)} \\ \\ \\ \dfrac{2 \sqrt{15}+5 \sqrt{6} }{3}$

RESPUESTA

$\boxed{\dfrac{2 \sqrt{15}+5 \sqrt{6} }{3}}$