Question

Write the reciprocal of $2+\sqrt{3}$.

Answer 1

$x=2+\sqrt{3}\frac{1}{x}=\frac{1}{2+\sqrt{3}}=\frac{1}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}}=\frac{2-\sqrt{3}}{4-3}=2-\sqrt{3}$

Reciprocal of $2+\sqrt{3}$ is $2-\sqrt{3}$ .