Question

Rationalise:
$\frac{2}{3-\sqrt{5}}$

• A. $\frac{3+\sqrt{5}}{2}$
• B. $\frac{2}{3+\sqrt{5}}$
• C. $\frac{3-\sqrt{5}}{2}$
• D. $\frac{9-\sqrt{5}}{2}$

Answer 1

The correct option is A $\frac{3+\sqrt{5}}{2}$

$\frac{2}{3-\sqrt{5}}=\frac{2}{3-\sqrt{5}}\times \frac{3+\sqrt{5}}{3+\sqrt{5}}=2\times (3+\sqrt{5})\frac{1}{3^2-5}=2\times (3+\sqrt{5})\frac{1}{4}=\frac{3+\sqrt{5}}{2}$