$\frac{\sqrt{80}}{\sqrt{5}}$
= $\sqrt{\frac{80}{5}}$
= $\sqrt{16}$
= 4

$\sqrt{\frac{4}{9}}·\sqrt{1}$
= $\sqrt{\frac{4}{9}·1}$
= $\sqrt{\frac{4}{9}}$
= $\frac{2}{3}$

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

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

${\left(\sqrt{10}-\sqrt{40}\right)}^2$ = ${\left(\sqrt{10}\right)}^2-2·\sqrt{10}·\sqrt{40}+{\left(\sqrt{40}\right)}^2$
= $10-2·\sqrt{10}·\sqrt{10·4}+40$
= $10-2·\sqrt{10}·\sqrt{10}·\sqrt{4}+40$
= $10-2·10·2+40$
= $10-40+40$
= $10$

$\sqrt{2x}·\sqrt{18x}$
= $\sqrt{2}·\sqrt{x}·\sqrt{18}·\sqrt{x}$
= $\sqrt{2}·\sqrt{18}·\sqrt{x}·\sqrt{x}$
= $\sqrt{2}·\sqrt{2·9}·x$
= $\sqrt{2}·\sqrt{2}·\sqrt{9}·x$
= $2·3·x$
= $6x$

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

$\sqrt{28}-4\sqrt{28}$
= $-3\sqrt{28}$