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

$\sqrt{\frac{1}{27}}·\sqrt{3}$
= $\sqrt{\frac{1}{27}·3}$
= $\sqrt{\frac{1}{9}·1}$
= $\sqrt{\frac{1}{9}}$
= $\frac{1}{3}$

$\sqrt{10}·\left(\sqrt{10}+\sqrt{360}\right)$
= $\sqrt{10}·\sqrt{10}+\sqrt{10}·\sqrt{360}$
= $10+\sqrt{10}·\sqrt{10·36}$
= $10+\sqrt{10}·\sqrt{10}·\sqrt{36}$
= $10+10·6$
= $10+60$
= $70$

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

${\left(\sqrt{2}-\sqrt{32}\right)}^2$ = ${\left(\sqrt{2}\right)}^2-2·\sqrt{2}·\sqrt{32}+{\left(\sqrt{32}\right)}^2$
= $2-2·\sqrt{2}·\sqrt{2·16}+32$
= $2-2·\sqrt{2}·\sqrt{2}·\sqrt{16}+32$
= $2-2·2·4+32$
= $2-16+32$
= $18$

$\sqrt{81x}+5\sqrt{x}$
= $\sqrt{81}·\sqrt{x}+5\sqrt{x}$
= $9\sqrt{x}+5\sqrt{x}$
= $14\sqrt{x}$

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

$-\sqrt{22}-9\sqrt{22}$
= $-10\sqrt{22}$