Question

Rationalise the denomenator- 7+3√5/ 7-3√5

Answer 1

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