$\sqrt{5}·\sqrt{80}$
= $\sqrt{5}·\sqrt{5·16}$
= $\sqrt{5}·\sqrt{5}·\sqrt{16}$
= $5·4$
= $20$

$\frac{\sqrt{\mathrm{0,008}}}{\sqrt{\mathrm{0,2}}}$
= $\sqrt{\frac{0.008}{0.2}}$
= $\sqrt{\frac{0.08}{2}}$
= $\sqrt{\mathrm{0,04}}$
= 0.2

$\left(\sqrt{50}+\sqrt{2}\right)·\sqrt{2}$
= $\sqrt{50}·\sqrt{2}+\sqrt{2}·\sqrt{2}$
= $\sqrt{2·25}·\sqrt{2}+2$
= $\sqrt{25}·\sqrt{2}·\sqrt{2}+2$
= $5·2+2$
= $10+2$
= $12$

Nach der 3. binomischen Formel ((a+b)(a-b)=a²-b²) gilt:

$\left(\sqrt{9}+6\right)·\left(\sqrt{9}-6\right)$ = ${\left(\sqrt{9}\right)}^2-6^2$
= $9-36$
= $-27$

$2\sqrt{x}+\sqrt{49x}$
= $2\sqrt{x}+\sqrt{49}·\sqrt{x}$
= $2\sqrt{x}+7\sqrt{x}$
= $9\sqrt{x}$

Wir können die $\sqrt{22}$ wie Einheiten behandeln und einfach verrechnen.

$5\sqrt{22}-\sqrt{22}$
= $4\sqrt{22}$