Question

1) 5/root 8-root2
2) 5+ root 5 divided by5- root 2
3) 3+2root2 divided by 6-root3

Answer 1

Answer:

$= 5 \sqrt{8} - \sqrt{2} \\ = 5 \sqrt{4 \times 2} - \sqrt{2} \\ = 10 \sqrt{2} - \sqrt{2} \\ = 9 \sqrt{2} \\ \frac{5 + \sqrt{5} }{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } \\ \frac{5(5 + \sqrt{2}) + \sqrt{5}(5 + \sqrt{2} ) }{5 {}^{2} - ( \sqrt{2} ) {}^{2} } \\ 25 + 5 \sqrt{2} + 5 \sqrt{5} + \sqrt{10} \div 25 - 2 \\ \frac{25 + 5 \sqrt{2} + 5 \sqrt{5 } + \sqrt{10} }{23}$