Question

Rationalize the denominator.



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Answer 1

$\frac{6}{2 \sqrt{3} + \sqrt{6} } \\ = \frac{6 \times (2 \sqrt{3} - \sqrt{6} ) }{(2 \sqrt{3} + \sqrt{6}) \times (2 \sqrt{3} - \sqrt{6} ) } \\ = \frac{12 \sqrt{3} - 6 \sqrt{6} }{ {(2 \sqrt{3} )}^{2} - {( \sqrt{6}) }^{2} } \\ = \frac{12 \sqrt{3} - 6 \sqrt{6} }{(4 \times 3) - 6} \\ = \frac{12 \sqrt{3} - 6 \sqrt{6} }{12 - 6} = \frac{12 \sqrt{3} - 6 \sqrt{6} }{6}$

Using identity :

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

$where \\ a = 2 \sqrt{3} \\ and \: \: \: \: b = \sqrt{6}$

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