Question

rationalise the denominator 1/2+√3

Answer 1

the rationalising factor of 1/2+√3is 1/2-√3

Answer 2

$\bf \underline{ \underline \bold{Question}}$

$\sf \longrightarrow \bigstar Rationalise \: the \: denominator \: of \: \frac{1}{2 + \sqrt{3} }$

$\bf \underline{ \underline \bold{Formula\: Used}}$

$\bigstar {\underline {\boxed { \bf {\green\:(a+ \sqrt{b} )(a- \sqrt{b}) ➞ \: a {}^{2} -b }}}} \bigstar$

$\bf \underline{ \underline \bold{Substitution}}$

$\sf \leadsto \frac{1}{2 + \sqrt{3} }$

$\sf Applying \: the \: Formula,\:$

$\sf \leadsto \frac{1 \times (2- \sqrt{3} )}{(2+ \sqrt{3} )(2- \sqrt{3}) }$

$\sf \leadsto \frac{2- \sqrt{3} }{2 {}^{2} - ( \sqrt{3} ) {}^{2} }$

$\sf \leadsto \frac{2- \sqrt{3} }{4 - 3 }$

$\sf \leadsto \frac{2- \sqrt{3} }{1}$

$\sf \leadsto 2 - \sqrt{3}$

$\sf\: Hence,\: the \: required \: value \: is \: \bold {2- \sqrt{3} }$