8. Let $i$ and $j$ represent the unit vectors on the $x$-axis and $y$-axis of a Cartesian coordinate system, respectively, and
$$
|a-i|+|a-2 j|=\sqrt{5} \text {. }
$$

Then the range of $|a+2 i|$ is ( ).
(A) $[2 \sqrt{2}, 3]$
(B) $\left[\frac{6 \sqrt{5}}{5}, 2 \sqrt{2}\right]$
(C) $[\sqrt{5}, 4]$
(D) $\left[\frac{6 \sqrt{5}}{5}, 3\right]$
8. D.

Since the endpoint of vector $a$ lies on the line segment $2 x+y-2=0(0 \leqslant x \leqslant 1)$ that satisfies $|a-i|+|a-2 j|=\sqrt{5}$, the maximum value of $|a+2 i|$ is the distance between the point $(-2,0)$ and $(1,0)$, which is 3, and the minimum value is the distance from the point $(-2,0)$ to the line segment, which is $\frac{6 \sqrt{5}}{5}$.