Question

$3 \sqrt{2} \div \sqrt{10 + \sqrt{3} }$
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Answer 1

$3 \sqrt{2} \div \sqrt{10 + \sqrt{3} } \\ \\ = \frac{3 \sqrt{2} }{ \sqrt{10 + \sqrt{3} } } \\ \\ = \frac{3 \sqrt{2} }{ (\sqrt{10 + \sqrt{3} } )} \frac{(\sqrt{10 + \sqrt{3} })}{(\sqrt{10 + \sqrt{3} })} \\ \\ = \frac{3 \sqrt{20 + 2 \sqrt{3} } }{10 + \sqrt{3} } \\ \\ = \frac{3 (\sqrt{20 + 2 \sqrt{3} } )}{(10 + \sqrt{3}) } \frac{(10 - \sqrt{3}) }{(10 - \sqrt{3}) } \\ \\ = \frac{30 \sqrt{20 + 2 \sqrt{3} } - 3 \sqrt{60 + 6 \sqrt{3} } }{97}$

hope it helps