Question

сократите дробь 5- под корнем5/под корнем10 - под корнем2

Answer 1

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