Question

2√2-3√5
_______
5√5-√2
solve in steps

Answer 1

$\frac{2 \sqrt{2} - 3 \sqrt{5} }{5 \sqrt{5} - \sqrt{2} } \times \frac{5 \sqrt{5} + \sqrt{2} }{5 \sqrt{5} + \sqrt{2} } \\ \: = \frac{(2 \sqrt{2} - 3 \sqrt{5})(5 \sqrt{5} + \sqrt{2}) }{125 - 2} \\ \: = \frac{4 - 75 - 3 \sqrt{10} + 10 \sqrt{10} }{123} \\ \: = \frac{7 \sqrt{10} - 71}{123}$