Question

simplify
$\frac{1}{2 + \sqrt{3} }$
​

Answer 1

$\huge\underline {\sf {Answer:}}$

$\underline {\bold {Given:}}$

• $\dfrac{1}{2+\sqrt3}$

$\underline {\bold {Solution:}}$

By rationalization:

$\implies \dfrac{1}{2+\sqrt3}$

$\implies \dfrac{1}{2 + \sqrt3} \times \dfrac{2 - \sqrt3}{2 - \sqrt3}$

$\implies \dfrac{2 -\sqrt3}{2^2 - \sqrt3 ^2}$

$\implies \dfrac{2 - \sqrt3}{4 - 3}$

$\boxed{\implies{\boxed{2 - \sqrt3}}}$

Answer 2

Answer:

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