Question

Rationalise the denominator :
7 + 3√5/7 - 3√5

Answer 1

$\sf \implies \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \\ \\ \sf \implies \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \times \frac{7 + 3 \sqrt{5}}{7 + 3 \sqrt{5}} \\ \\ \sf \implies \frac{ {(7 + 3 \sqrt{5} )}^{2} }{ {(7)}^{2} - {(3 \sqrt{5} )}^{2} } \\ \\ \sf \implies \frac{ {(7)}^{2} + {(3 \sqrt{5}) }^{2} - 2 \times 7 \times 3 \sqrt{5} }{49 - 9(5)} \\ \\ \sf \implies \frac{49 + 9(5) - 42 \sqrt{5} }{49 - 45} \\ \\ \sf \implies \frac{49 + 45 - 42 \sqrt{5} }{4} \\ \\ \sf \implies \frac{94 - 42 \sqrt{5} }{4} \\ \\ \sf \implies \frac{2(47 - 21 \sqrt{5}) }{4} \\ \\ \sf \implies \frac{47 - 21 \sqrt{5} }{2}$

$\large \fbox{ \fbox{ \sf \: \frac{47 - 21 \sqrt{5} }{2} \: }}$