Question

rationalize the denominator of 1/8-5√2​

Answer 1

$\frac{1}{8 - 5 \sqrt{2} }$

$= \frac{1}{8 - 5 \sqrt{2} } \times \frac{8 + 5 \sqrt{2} }{8 + 5 \sqrt{2} }$

$= \frac{8 + 5 \sqrt{2} }{ {8}^{2} - ( {5 \sqrt{2}) }^{2} }$

$= \frac{8 + 5 \sqrt{2} }{64 - 25 \times 2}$

$= \frac{8 + 5 \sqrt{2} }{64 - 50}$

$= \frac{8 + 5 \sqrt{2} }{14}$