I don't know how to approach this...

$d\ =\ \sqrt{(1-5)^2+(\sqrt2-\sqrt8)^2}$          But   $\sqrt2-\sqrt8\ \neq\ -2$    !!

$d\ =\ \sqrt{(1-5)^2+(\sqrt2-2\sqrt2)^2}$          because   $\sqrt8\ =\ 2\sqrt{2}$

$d\ =\ \sqrt{(1-5)^2+(-\sqrt2\,)^2}$          because   x - 2x  =  -x    so     $\sqrt2-2\sqrt2\ =\ -\sqrt2$

$d\ =\ \sqrt{(-4)^2+(-\sqrt2\,)^2}$          because  1 - 5  =  -4

$d\ =\ \sqrt{16+2}$          because   $(-4)^2=16$     and     $(-\sqrt2)^2=2$

$d\ =\ \sqrt{18}$

$d\ =\ 3 \sqrt{2}$_