Question

Rationalise the denominate
5by√3-√5
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Answer 1

Answer:

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