Question

Rationalise the denominator of (√3 -√5) / (√3 +√5) ​

Answer 1

Answer:

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Answer 2

$\frac{ \sqrt{3} - \sqrt{5} }{ \sqrt{3} + \sqrt{5} } \\ \\ = \frac{ \sqrt{3} - \sqrt{5} }{ \sqrt{3} + \sqrt{5} } \times \frac{ \sqrt{3} - \sqrt{5} }{ \sqrt{3} - \sqrt{5} } \\ \\ = \frac{( { \sqrt{3} - \sqrt{5}) }^{2} }{( { \sqrt{3} )}^{2} - ( { \sqrt{5} )}^{2} } \\ \\ = \frac{3 - 2. \sqrt{3}. \sqrt{5} \: + 5 }{3 - 5} \\ \\ = \frac{8 - 2 \sqrt{15} }{ - 2} \\ \\ = \frac{2(4 - \sqrt{15} )}{ - 2} \\ \\ = - (4 - \sqrt{15} ) \\ \\ = - 4 + \sqrt{15} \\ \\ = \sqrt{15} - 4$