Question

rationalise the denominator of 2by3root -5root

Answer 1

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

Answer 2

$\frac{2}{ \sqrt{3}- \sqrt{5} }$   

by Rationalization,

$\frac{2}{ \sqrt{3}- \sqrt{5} }$×$\frac{ \sqrt{3} + \sqrt{5} }{ \sqrt{3} + \sqrt{5} }$

$\frac{2 \sqrt{3} + 2 \sqrt{5} }{( \sqrt{3})^2 - ( \sqrt{5} )^2}$

$\frac{2 \sqrt{3} + 2 \sqrt{5} }{3 - 5 }$

$\frac{2 ( \sqrt{3} + \sqrt{5} }{-2 }$


-√3 - √5 



i hope this will help you


(-: