Answer
$e=\dfrac{\sqrt2}{2} \approx 0.71$
Work Step by Step
The given ellipse has $a^2=8$ and $b^2=4$.
Solve for $c$ using the formula $c^2=a^2-b^2$ to obtain:
\begin{align*}
c^2&=a^2-b^2\\
c^2&=8-4\\
c^2&=4\\
c&=\sqrt4\\
c&=2 \quad \quad \text{(since $a$ is non-negative, we only take the principal root)}
\end{align*}
The eccentricity of the ellipse can be computed as: $e=\dfrac{c}{a}$
Solve for $a$:
\begin{align*}
a^2&=8\\
a&=\sqrt 8\\
a&=\sqrt{4(2)}\\
a&=2\sqrt2
\end{align*}
Thus,
$$e=\dfrac{2}{2\sqrt2}=\dfrac{2}{2\sqrt2}\cdot \dfrac{\sqrt2}{\sqrt2}=\dfrac{\sqrt2}{2} \approx 0.71$$
