Question

rationalise √6/√2+√3​

Answer 1

Step-by-step explanation:

$\bf \frac{ \sqrt{6} }{ \sqrt{2} + \sqrt{3} } \\ \\ \bf \mapsto: \frac{ \sqrt{6} ( \sqrt{2} - \sqrt{3} ) }{( \sqrt{2} + \sqrt{3} )( \sqrt{2} - \sqrt{3} )} \\ \\ \bf \mapsto: \frac{ \sqrt{6} \times \sqrt{2} - \sqrt{6} \times \sqrt{3} }{( { \sqrt{2}) }^{2} - { (\sqrt{3}) }^{2} } \\ \\ \bf \mapsto: \frac{ \sqrt{12} - \sqrt{18} }{2 - 3} \\ \\ \bf \mapsto: \frac{ \sqrt{2 \times 2 \times 3} - \sqrt{3 \times 2 \times 3} }{ - 1} \\ \\ \bf \mapsto: \frac{2 \sqrt{3} -3 \sqrt{2} }{ - 1} \\ \\ \bf \mapsto: - 2 \sqrt{3} + 3 \sqrt{2} \\ \\ \boxed{\bf \mapsto: 3 \sqrt{2 - 2 \sqrt{3} } \ddot \smile}$