Question

1√6/√2+√3 simplify the denominator
​

Answer 1

Step-by-step explanation:

$\sqrt{2} \: - \sqrt{3}$

Answer 2

$\huge \dag \: \: \: \: \: \bf \frac{1 \sqrt{6} }{ \sqrt{2} + \sqrt{3} } \\ \\ \to \sf \frac{ \sqrt{6} }{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } \\ \\ \to \sf \frac{ \sqrt{6}( \sqrt{2} - \sqrt{3} ) }{ {( \sqrt{2} )}^{2} - {( \sqrt{3} )}^{2} } \\ \\ \to \sf \frac{ \sqrt{12} - \sqrt{18} }{2 - 3} \: \: \: \to \frac{2 \sqrt{3} - 3 \sqrt{2} }{ - 1} \\ \\ \to \sf \: \: \: - (2 \sqrt{3} - 3 \sqrt{2} ) \\ \to \sf \: \: \: - 2 \sqrt{3} + 3 \sqrt{2} \\ \to \sf \: \: \: \red{3 \sqrt{2} - 2 \sqrt{3} }$

$\boxed{\rm Or,\: \:\: \:\: \: \:\: \:\: \: \:\: \:\: \:\: \:\: \:\: \: \:\: \: \:\: \:\: \: \:\: \:\: \:\:\: \:\: \: \:}$

$\huge \dag \: \: \: \bf \frac{1 + \sqrt{6} }{ \sqrt{2} + \sqrt{3} } \\ \\ \to \sf \frac{1 + \sqrt{6} }{ \sqrt{2} + \sqrt{3} } \times \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2} - \sqrt{3}} \\ \\ \to \sf \frac{1(\sqrt{2} - \sqrt{3}) + \sqrt{6} (\sqrt{2} - \sqrt{3})}{ {( \sqrt{2} )}^{2} - {( \sqrt{3} )}^{2} } \\ \\ \to \sf \frac{\sqrt{2} - \sqrt{3} + \sqrt{12} - \sqrt{18} }{2 - 3} \\ \\ \to \sf \: \: \frac{ \sqrt{2} - \sqrt{3} + 2 \sqrt{3} - 3 \sqrt{2} }{ - 1} \\ \\ \to \sf \: \: - [(1 - 3) \sqrt{2} + (2 - 3) \sqrt{3} ] \\ \to \sf \: \: - [ - 2 \sqrt{2} + ( - 1 \sqrt{3}) ] \\ \to \sf \: \: - [ - 2 \sqrt{2} - \sqrt{3} ] \\ \to \sf \: \: \red{2 \sqrt{2} + \sqrt{3} }$