Question

rationalise the denominator of the following​

Answer 1

Answer:

2+root3

Step-by-step explanation:

1/2-root3

1/(2-root3)

2+root3/4-3

2+root3

Answer 2

Answer :

$\tt \: 2 + \sqrt{3}$

Solution:

Rationalise the denominator :

$\tt \dfrac{1}{2 - \sqrt{3} }$

To rationalize the denominator , we multiply both numerator and denominator with a term that is exactly same as denominator but with an opposite sign .

To rationalize , $\tt \frac{1}{2 - \sqrt{3}}$ , we multiply both numerator and denominator with $\tt 2+ \sqrt{3}$ .

$\tt \therefore \dfrac{1}{2 - \sqrt{3} } \times \dfrac{2 + \sqrt{3} }{2 + \sqrt{3} }$

$\tt \implies \dfrac{2 + \sqrt{3} }{(2 - \sqrt{3})(2 + \sqrt{3} )} \\ \\ \tt \implies \frac{2 + \sqrt{3} }{ ({2})^{2} - { (\sqrt{3}) }^{2} } \\ \\ \tt \implies \frac{2 + \sqrt{3} }{4 - 3} \\ \\ \tt \implies 2 + \sqrt{3}$

${ \rm{ \therefore \: rationalising \: denominator \: of \: \frac{1}{2 - \sqrt{3} } }} \\ \\ { \rm\: gives \: 2 + \sqrt{3}. }$