Question

√6+√5/√6-√5 number system and solved the problem

Answer 1

$\frac{ \sqrt{6} + \sqrt{5} }{ \sqrt{6} - \sqrt{5} }$
_______________________________________________

 By Rationalization,




$\frac{ \sqrt{6}+ \sqrt{5} }{ \sqrt{6} - \sqrt{5} }$×$\frac{ \sqrt{6}+ \sqrt{5} }{ \sqrt{6} + \sqrt{5} }$


_________________________ 


On denominator,

By Formula, $a^2 -b^2 = (a+b)(a-b)$

On nominator,

By Formula, $(a+b)^2 = a^2 + b^2 +2ab$
____________________________________________


$\frac{ \sqrt{6}+ \sqrt{5} }{ \sqrt{6}- \sqrt{5} }$×$\frac{ \sqrt{6} + \sqrt{5} }{ \sqrt{6}+ \sqrt{5} }$



$\frac{( \sqrt{6}+ \sqrt{5})^2 }{( \sqrt{6})^2 - (\sqrt{5})^2 }$


Applying  Formula


$\frac{6 + 5 + 2\sqrt{30} }{6-5}$



$\frac{11 + 2 \sqrt{30} }{1}$



$11 + 2 \sqrt{30}$



i hope this will help you



-by ABHAY