Question

rationalize the following 2+√3/2-√3​

Answer 1

Step-by-step explanation:

$\dfrac{2 + \sqrt{3} }{2 - \sqrt{3} } \\ = \dfrac{(2 + \sqrt{3}) }{(2 - \sqrt{3} )} \\ = \dfrac{(2 + \sqrt{3} ) \: (2 + \sqrt{3} )}{(2 - \sqrt{3} ) \: (2 + \sqrt{3} )} \\ = \dfrac{ {(2 + \sqrt{3} )}^{2} }{ {(2)}^{2} - {( \sqrt{3} )}^{2} } \\ = \dfrac{ {(2)}^{2} + {( \sqrt{3}) }^{2} + 2 \: (2) \: ( \sqrt{3} )}{(4 - 3)} \\ = \dfrac{4 + 3 + 4 \sqrt{3} }{1} \\ = 7 + 4 \sqrt{3} \\ \bold {\large {\underline{ \pink{formula \: used}}}} \large{\bold{\pink{\longrightarrow}}} \\ \bold{\blue{1. {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}} \\ \red{\bold{2. \: {x}^{2} - {y}^{2} = (x + y)(x - y)}}$