Question

5 upon √3-√5 rationalise the denominator

PLEASE HELP!!!!!
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Answer 1

Denominator of \frac{5}{ \sqrt{3} - \sqrt{5} } is (\sqrt{3} - \sqrt{5})

Here, the conjugate of denominator (\sqrt{3} - \sqrt{5}) is (\sqrt{3} + \sqrt{5})

= \frac{5}{ \sqrt{3} - \sqrt{5} } \times \frac{ \sqrt{3} + \sqrt{5} }{ \sqrt{3} + \sqrt{5} } \: \: \: (by \: \: rationalisation) \\ \\ \\ = \frac{5( \sqrt{3} + \sqrt{5} ) }{ {( \sqrt{3} )}^{2} - {( \sqrt{5}) }^{2} } \: \: \: \: \: ( \therefore \: (a - b)(a + b) = {a}^{2} - {b}^{2} \: ) \\ \\ \\ = \frac{5( \sqrt{3} + \sqrt{5} ) }{3 - 5} \\ \\ \\ = - \frac{5}{2} ( \sqrt{3} + \sqrt{5} )

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Answer 2

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