Question

Rationalise denominator 1/√3+2​

Answer 1

Here you go!

$\longrightarrow{\green{}}$ $\frac{1}{ \sqrt{3} + 2 }$

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

$\longrightarrow{\green{}}$ $\frac{ \sqrt{3} - 2}{ ({ \sqrt{3} })^{2} - ({2})^{2} }$

$\longrightarrow{\green{}}$ $\frac{ \sqrt{3} - 2}{3 - 4}$

$\longrightarrow{\green{}}$ $\frac{ \sqrt{3} - 2 }{ - 1}$

$\longrightarrow{\green{}}$ $- ( \sqrt{3} - 2)$

$\longrightarrow{\green{}}$ $- \sqrt{3} + 2$

Note:

$(a + b)(a - b) = {a}^{2} - {b}^{2}$