Question

Rationalize the denominator of 5/(7+√5)​

Answer 1

\begin{gathered} \frac{5}{ \sqrt{7} - \sqrt{2} } \\ = \frac{5}{ \sqrt{7} - \sqrt{2} } \times \frac{ \sqrt{7} + \sqrt{2} }{ \sqrt{7} + \sqrt{2} } \\ = \frac{(5) \times ( \sqrt{7} + \sqrt{2}) }{ {( \sqrt{7} )}^{2} - {( \sqrt{2}) }^{2} } \\ = \frac{(5) \times ( \sqrt{7} + \sqrt{2}) }{7 - 2} \\ = \frac{(5) \times ( \sqrt{7} + \sqrt{2}) }{(5)} \\ = \sqrt{7} + \sqrt{2} \end{gathered}7−25=7−25×7+27+2=(7)2−(2)2(5)×(7+2)=7−2(5)×(7+2)=(5)(5)×(7+2)=7+2