Question

Rationalise the denominator of root 3 - 1 divide root 3 + 1

Answer 1

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Rationalise the denominator of root 3 - 1 divide root 3 + 1

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${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ (a + b)(a - b) = {a}^{2} - {b}^{2}$

$\boxed{Now}$,

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

$\boxed{Rationalizing\:the \: dinominator}$

we get,

$\frac{ { \sqrt{3} }^{2} + {1}^{2} + 2( \sqrt{3} )(1) }{ {( \sqrt{3} }^{2}) - ( {1}^{2} )}$

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

$\frac{4 + 2 \sqrt{3} }{2}$

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

$2 + \sqrt{3}$