$\frac{\sqrt{90}}{\sqrt{10}}$
= $\sqrt{\frac{90}{10}}$
= $\sqrt{9}$
= 3

$\frac{\sqrt{480}}{\sqrt{\mathrm{0,003}}}$
= $\sqrt{\frac{480}{0.003}}$
= $\sqrt{\frac{480.000}{3}}$
= $\sqrt{160000}$
= 400

$\left(\sqrt{18}+\sqrt{2}\right)·\sqrt{2}$
= $\sqrt{18}·\sqrt{2}+\sqrt{2}·\sqrt{2}$
= $\sqrt{2·9}·\sqrt{2}+2$
= $\sqrt{9}·\sqrt{2}·\sqrt{2}+2$
= $3·2+2$
= $6+2$
= $8$

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

${\left(\sqrt{3}-\sqrt{108}\right)}^2$ = ${\left(\sqrt{3}\right)}^2-2·\sqrt{3}·\sqrt{108}+{\left(\sqrt{108}\right)}^2$
= $3-2·\sqrt{3}·\sqrt{3·36}+108$
= $3-2·\sqrt{3}·\sqrt{3}·\sqrt{36}+108$
= $3-2·3·6+108$
= $3-36+108$
= $75$

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

Wir können die $\sqrt{50}$ wie Einheiten behandeln und einfach verrechnen.

$4\sqrt{50}+2\sqrt{50}$
= $6\sqrt{50}$