Question

Express 3/√3 - √2+√5 with a rational denominator

Answer 1

Solution:-

$\frac{3}{ \sqrt{3} - \sqrt{2} + \sqrt{5} } \\ \frac{3}{ \sqrt{3} - \sqrt{2} + \sqrt{5} } \times \frac{ \sqrt{3} + \sqrt{2} + \sqrt{5} }{ \sqrt{3} + \sqrt{2} + \sqrt{5} } \\ \frac{3( \sqrt{3 } + \sqrt{2} + \sqrt{5}) }{3 - ( { \sqrt{2 } + \sqrt{5} )}^{2} } \\ \\ \frac{3 \sqrt{3} + 3 \sqrt{2} + \sqrt{5} }{3 -( 2 + 5 + 2 \sqrt{10}) } \\ \frac{3 \sqrt{3} + 3 \sqrt{2} + 3 \sqrt{5} }{ - 4 - 2 \sqrt{10} }$