Question

Rationalise the denominator : √3+√5/√3-√5

Answer 1

$\frac{ \sqrt{3} + { \sqrt{5} } }{ \sqrt{3} - \sqrt{5} }$
$= \frac{ (\sqrt{3} + \sqrt{5})( \sqrt{3} + \sqrt{5} )}{ (\sqrt{3} - \sqrt{5})( \sqrt{3} + \sqrt{5} ) }$
$= \frac{ { \sqrt{3} }^{2} + (2 \times \sqrt{3} \times \sqrt{5} ) + { \sqrt{5} }^{2} }{ { \sqrt{3} }^{2} - { \sqrt{5} }^{2} }$
$= \frac{3 + 2 \sqrt{15} + 25}{3 - 5}$
$= \frac{28 + 2 \sqrt{15} }{ - 2}$
$= \frac{ 2(14 + \sqrt{15}) }{ - 2}$
$= \frac{14 + \sqrt{15} }{ - 1}$
$= - (14 + \sqrt{15} )$
$= - 14 - \sqrt{15}$




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