Question

Rationalize the denominated of 1/√7-√6

Answer 1

$\frac{1}{ \sqrt{7} - \sqrt{6} } \times \frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} + \sqrt{6} } \\ = \frac{ \sqrt{7} + \sqrt{6} }{( \sqrt{7})^{2} -( \sqrt{6} ) ^{2} } \\ = \frac{ \sqrt{7} + \sqrt{6} }{7 - 6} \\ = \sqrt{7} + \sqrt{6}$

Answer 2

$\frac{1}{ \sqrt{7} - \sqrt{6} } \times \frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} + \sqrt{6} } \\ = \frac{ \sqrt{7} + \sqrt{6} }{( \sqrt{7}) ^{2} - ( \sqrt{6}) ^{2} } \\ = \frac{ \sqrt{7} + \sqrt{6} }{7 - 6} \\ = \frac{ \sqrt{7} + \sqrt{6} }{1} \\ = \sqrt{7} + \sqrt{6}$