Question

ratinalize the denominator 1 /2+root 3

Answer 1

$\bf \huge \underbrace{Answer : } \\ \\ \sf \implies \: \frac{1}{2 + \sqrt{3} } \\ \\ \sf \implies \: \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \sf \implies \: \frac{2 - \sqrt{3} }{ {(2)}^{2} - {( \sqrt{3} })^{2} } \\ \\ \sf \implies \: \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \sf \implies \: \frac{2 - \sqrt{3} }{1} \\ \\ \sf \implies \:2 - \sqrt{3}$

Answer 2

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

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

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

$= \frac{2 - \sqrt{3} }{4 - 3}$

$= \frac{2 - \sqrt{3} }{1}$

$= 2 - \sqrt{3}$