$\sqrt{10}·\sqrt{360}$
= $\sqrt{10}·\sqrt{10·36}$
= $\sqrt{10}·\sqrt{10}·\sqrt{36}$
= $10·6$
= $60$

$\sqrt{5}·\sqrt{\frac{1}{20}}$
= $\sqrt{5·\frac{1}{20}}$
= $\sqrt{1·\frac{1}{4}}$
= $\sqrt{\frac{1}{4}}$
= $\frac{1}{2}$

$\left(\sqrt{45}+\sqrt{5}\right)·\sqrt{5}$
= $\sqrt{45}·\sqrt{5}+\sqrt{5}·\sqrt{5}$
= $\sqrt{5·9}·\sqrt{5}+5$
= $\sqrt{9}·\sqrt{5}·\sqrt{5}+5$
= $3·5+5$
= $15+5$
= $20$

Nach der 2. binomischen Formel ((a-b)²=a²-2ab+b²) gilt:

${\left(\sqrt{5}-\sqrt{80}\right)}^2$ = ${\left(\sqrt{5}\right)}^2-2·\sqrt{5}·\sqrt{80}+{\left(\sqrt{80}\right)}^2$
= $5-2·\sqrt{5}·\sqrt{5·16}+80$
= $5-2·\sqrt{5}·\sqrt{5}·\sqrt{16}+80$
= $5-2·5·4+80$
= $5-40+80$
= $45$

$\frac{\sqrt{18x}}{\sqrt{2x}}$
= $\frac{\sqrt{18}·\sqrt{x}}{\sqrt{2}·\sqrt{x}}$
= $\frac{\sqrt{18}}{\sqrt{2}}$
= $\sqrt{\frac{18}{2}}$
= $\sqrt{9}$
= $3$

Wir können die $\sqrt{28}$ wie Einheiten behandeln und einfach verrechnen.

$18\sqrt{28}+8\sqrt{28}$
= $26\sqrt{28}$