Question

How to rationalise 1/8+5root2

Answer 1

$\frac{1}{8 + 5 \sqrt{2} } \\ \\ = \frac{1}{8 + 5 \sqrt{2} } \times \frac{8 - 5 \sqrt{2} }{8 - 5 \sqrt{2} } \\ \\ = \frac{8 - 5 \sqrt{2} }{ {8}^{2} - ( {5 \sqrt{2}) }^{2} } \\ \\ = \frac{8 - 5 \sqrt{2} }{64 - 50} \\ \\ = \frac{8 - 5 \sqrt{2} }{14}$