Algebra roots problem

I have a problem. This seems simple but I find it hard to solve because I searched this problem on the internet on how can this problem be solved with steps but I never found any. There is one, but there is a payment and I couldn't afford yet so I'm hoping this website can help me figure this out.


How can this be simplified with steps.


$\sqrt{5} \pm \sqrt{8} = \sqrt{5} \pm \sqrt{4 \times 2}$

$\sqrt{5} \pm \sqrt{8} = \sqrt{5} \pm 2\sqrt{2}$

$\sqrt{5} \pm \sqrt{8} = \begin{cases} \sqrt{5} + 2\sqrt{2} & \text{and} \\ \sqrt{5} - 2\sqrt{2} \end{cases}$