Question

$\frac{1}{2+\sqrt{3}}$ on simplifying is ___

• A. $4$
• B. $2-\sqrt{3}$
• C. $4-\sqrt{3}$
• D. $2\sqrt{3}$

Answer 1

The correct option is B

$2-\sqrt{3}$

$\frac{1}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}}$

$=\frac{2-\sqrt{3}}{(2{)}^2-(\sqrt{3}{)}^2}$ (The denominator is in the form $a^2-b^2$)

$=\frac{2-\sqrt{3}}{4-3}$

$=2-\sqrt{3}$