Question

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

Answer 1

Answer:

$\frac{5}{ \sqrt{3} - \sqrt{5} } \\ = \frac{5}{ \sqrt{3} - \sqrt{5} } \times \frac{ \sqrt{3} + \sqrt{5} }{ \sqrt{3} + \sqrt{5} } \\ = \frac{5 \sqrt{3} + 5 \sqrt{5} }{ { \sqrt{3} }^{2} - { \sqrt{5} }^{2} } \\ = \frac{5 \sqrt{3} + 5 \sqrt{5} }{3 - 5} \\ = \frac{5 \sqrt{3} + 5 \sqrt{5} }{ - 2} \\ = \frac{ - 5 \sqrt{3} - 5 \sqrt{5} }{2}$

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