The discriminant of the equation \((-2 \sqrt{2})^2-4(1)(1)=8-4=4 > 0\) and \(a\) perfect square, so roots are real and different but we can't say that roots are rational because coefficients are not rational therefore.
\(\frac{\sqrt{2 \sqrt{2} \pm \sqrt{(2 \sqrt{2})^2-4}}}{2}=\frac{2 \sqrt{2} \pm 2}{2}=\sqrt{2} \pm 1\)
this is irrational \(\therefore\) the roots are real and different.