Question

rationalize the denominator of root 7 - root 5 / root 7 + root 5 solve

Answer 1

$\frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} }$


By Rationalization,

$\frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} } \times \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} - \sqrt{5} } \\ \\ \\ \\ = > \frac{ {( \sqrt{7} - \sqrt{5} )}^{2} }{ {( \sqrt{7}) }^{2} - {( \sqrt{5}) }^{2} } \\ \\ \\ \\ => \frac{7 + 5 - 2 \sqrt{35} }{7 - 5 } \\ \\ \\ => \frac{12 - 2 \sqrt{35} }{2} \\ \\ \\ = > 6 - \sqrt{35}$