Question

Rationalise the denominator

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

Answer 1

Hola Mate!!

Your answer :-

$= > \frac{ \sqrt{5} }{ \sqrt{5} - \sqrt{3} } \\ \\ = > \frac{ \sqrt{5} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ \\ = > \frac{ \sqrt{5} ( \sqrt{5} + \sqrt{3}) }{( { \sqrt{5} )}^{2} - ({ \sqrt{3} )}^{2} } \\ \\ = > \frac{5 + \sqrt{15} }{5 - 3} \\ \\ = > \frac{ 5 + \sqrt{15} }{2}$

☆ Hope it helps ☆

Answer 2

Hey !

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↪√ 5 / √ 5 - √ 3

↪√ 5 / √ 5 - √ 3 ( √ 5 + √ 3 / √ 5 + √3 )

↪ Using the identity in denominator !!

↪ (a + b) (a - b) = a ^2 - b ^2

↪√ 5 ( √ 5 + √ 3 ) / √ 5 ^ 2 - √ 3 ^2

↪5 + √ 15 / 5 - 3

↪ 5 + √ 15 / 2

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