Question

Rationalize and simplify the expression
$\frac{1}{2+\sqrt{3}}$

• A. $\sqrt{2}+\sqrt{3}+\sqrt{5}$
• B. $2-\sqrt{3}$
• C. $1+\sqrt{5}$
• D. $1+\sqrt{3}$

Answer 1

The correct option is B $2-\sqrt{3}$

$\frac{1}{2+\sqrt{3}}$
$=\frac{1}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}}Now,(a-b)\times (a+b)=a^2-b^2=\frac{2-\sqrt{3}}{4-3}=\frac{2-\sqrt{3}}{1}=2-\sqrt{3}$