Question

 сократите  $frac{5- sqrt{5} }{ sqrt{10-5 sqrt{2} } }$

Answer 1

$frac{5- sqrt{5}}{sqrt{10}-5 sqrt{2}}=frac{ sqrt{5*5}- sqrt{5}}{sqrt{5*2}-sqrt{5*5*2}}=frac{ sqrt{5}*(sqrt{5}-1)}{sqrt{5*2}*(1-sqrt{5})}=- frac{1}{sqrt{2}}=-frac{sqrt{2}}{2}.$