HI
$\displaystyle a+b=\sqrt{(1-\sqrt{5})^2}+\sqrt{(\sqrt{5}-\sqrt{20})^2}$
$\displaystyle =|1-\sqrt{5}|+|\sqrt{5}-\sqrt{20}|$
$\displaystyle =|1-\sqrt{5}+\sqrt{5}-\sqrt{20}|$
$\displaystyle =|1-\sqrt{20}|$
$\displaystyle =1-\sqrt{20}$ or $\displaystyle \sqrt{20}-1$
Since it must be positive , then take $\displaystyle \sqrt{20}-1$