Question

Evaluate the following expression:
$\frac{2+\sqrt{3}}{2-\sqrt{3}}$.

• A. $7+4\sqrt{3}$
• B. $7-4\sqrt{3}$
• C. $7$
• D. None of the above

Answer 1

The correct option is A $7+4\sqrt{3}$

On rationalising we get,
$\Rightarrow \frac{2+\sqrt{3}}{2-\sqrt{3}}=\frac{2+\sqrt{3}}{2-\sqrt{3}}\times \frac{2+\sqrt{3}}{2+\sqrt{3}}$
$\Rightarrow \frac{2+\sqrt{3}}{2-\sqrt{3}}=\frac{({2+\sqrt{3})}^2}{4-3}$
$\Rightarrow \frac{2+\sqrt{3}}{2-\sqrt{3}}=4+3+2\times 2\times \sqrt{3}$
$\Rightarrow \frac{2+\sqrt{3}}{2-\sqrt{3}}=7+4\sqrt{3}$