Question

rationalize under root 2 by under root 5 + under root 7​

Answer 1

Answer:

$\frac{ \sqrt{2} }{ \sqrt{5} + \sqrt{7} } \times \frac{ \sqrt{2} }{ \sqrt{5} - \sqrt{7} } \\ \\ = \geqslant (a + b) \: \: (a - b) = {a}^{2} \: - {b}^{2} \\ \\ = \geqslant \sqrt{2} \times \sqrt{2 } = 2 \\ \\ = \geqslant \frac{ \sqrt{2} }{ \sqrt{5 + \sqrt{7} } } \times \frac{ \sqrt{2} }{ \sqrt{5} - \sqrt{7} } \\ \\ = \geqslant \frac{2}{( \sqrt{5}) {}^{2} - ( \sqrt{7} ) {}^{2} } \\ \\ = \geqslant \frac{2}{5 - 7} \\ \\ = \geqslant \frac{2}{ - 2} \\ \\ = \geqslant - 1$