a)
$\sqrt[]{8-2\sqrt15}$ `+ \sqrt3`
⇔$\sqrt[]{5-2\sqrt5\sqrt3+3}$ `+\sqrt3`
⇔$\sqrt[]{(\sqrt5-\sqrt3)^2}$ `+\sqrt3`
⇔`|\sqrt5-\sqrt3|+\sqrt3`
⇔`\sqrt5-\sqrt3+\sqrt3`
⇔`\sqrt5`
b)
`\sqrt(8-2\sqrt5)-\sqrt5`
⇔ $\sqrt[]{4-2.2.\sqrt[]{5}+5}$ `-` $\sqrt[]{5}$
⇔$\sqrt[]{(2-\sqrt[]{5})^2}$ `-` $\sqrt[]{5}$
⇔`|2-\sqrt5|-\sqrt5`
⇔`\sqrt5-2-\sqrt5`
⇔`-2`