Question

(√5+√3)/(√5-√3) is equal to a+√30b

Answer 1

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ = \frac{( { \sqrt{5} + \sqrt{3} ) }^{2} }{( { \sqrt{5}) }^{2} - ( { \sqrt{3}) }^{2} } \\ = \frac{5 + 3 + 2 \sqrt{15} }{5 - 3} \\ = \frac{8 + 2 \sqrt{15} }{2} \\ = 4 + \sqrt{15} = 4 + \sqrt{15} \times \sqrt{2} \div \sqrt{2} \\ = 4 + \frac{ \sqrt{30} }{ \sqrt{2} } \\ =a + \sqrt{30} b \\ so \: a = 4 \\ b = \frac{1}{ \sqrt{2} }$