Question

Root √7+√6upon root √7-√6

Answer 1

$\frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} - \sqrt{6} } \\ = \frac{( \sqrt{7} + \sqrt{6})( \sqrt{7} + \sqrt{6} ) }{( \sqrt{7} - \sqrt{6})( \sqrt{7} + \sqrt{6} ) } \\ = \frac{( \sqrt{7} + \sqrt{6}) {}^{2} }{( \sqrt{7}) {}^{2} - ( \sqrt{6}) {}^{2} } \\ = \frac{( \sqrt{7} ) {}^{2} + 2 \sqrt{42} + (\sqrt{6} ) {}^{2} }{7 - 3} \\ = \frac{7 + 3 + 2 \sqrt{42} }{4} \\ = \frac{10 + 2 \sqrt{42} }{4}$

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