Question

Rationalize the denominator of 5/√3-√5​

Answer 1

Answer:

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

Answer 2

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