Question

Rationalise the denominator of 1/(2+V3).
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Answer 1

Step-by-step explanation:

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

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

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

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

$= 2 - \sqrt{3}$

Answer 2

Answer:

Step-by-step explanation:

$1/(2 + \sqrt{3} ) = 1/(2 + \sqrt{3} ) * 2 - \sqrt{3} /2 - \sqrt{3} \\ = 2 - \sqrt{3} /(2 + \sqrt{3} )(2 - \sqrt{3} )\\ = 2 - \sqrt{3}/2^2 - ( \sqrt{3})^2\\ = 2 - \sqrt{3}/4 - 3\\ = 2 - \sqrt{3}$

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