Question

$i) \: \frac{1}{7 - \sqrt{5} }$

Answer 1

$given \\ \frac{1}{7 - \sqrt{5} } \\ rationalise \: denominator \\ \frac{1}{7 - \sqrt{5} } \times \frac{7 + \sqrt{5} }{7 + \sqrt{5} } \\ as \: (a - b) \: (a + b) = {a}^{2} - {b}^{2} \\ \frac{7 + \sqrt{5} }{49 - 5} \\ = \frac{7 + \sqrt{5} }{44}$