Question

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

Answer 1

Step-by-step explanation:

√5+√3/√5-√3

=(√5+√3) (√5+√3)/(√5-√3) (√5+√3)

=(√5)^2+2.√5.√3+(√3)^2/(√5)^2-(√3)^2

=5+2√15+3/5-3

=8+2√15/2

=2(4+√15)/2

=4+√15

Answer 2

To rationalize -

$\sf{ \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }}$

Solution -

$\sf{ \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }} \\ \\ \sf{ \implies { \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } }} \\ \\ \sf{ \implies { \dfrac{ ( \sqrt{5} + \sqrt{3} ) ^ 2 }{ 2 } }} \\ \\ \sf{ \implies { \dfrac{ 8 + 2 \sqrt{15} }{ 2 } }} \\ \\ \sf{ \implies { 4 + \sqrt{5} }}$

This is the required answer .

AddiTiOnaL InFoRmAtIon -

$\sf{ \implies { ( \sqrt{a} - \sqrt{b} ) \times ( \sqrt{a} + \sqrt{b} ) = a - b }}$