$\sqrt{5}·\sqrt{180}$
= $\sqrt{5}·\sqrt{5·36}$
= $\sqrt{5}·\sqrt{5}·\sqrt{36}$
= $5·6$
= $30$

$\frac{\sqrt{1200}}{\sqrt{0.03}}$
= $\sqrt{\frac{1200}{0.03}}$
= $\sqrt{\frac{120.000}{3}}$
= $\sqrt{40000}$
= 200

$\sqrt{5}·\left(\sqrt{5}+\sqrt{20}\right)$
= $\sqrt{5}·\sqrt{5}+\sqrt{5}·\sqrt{20}$
= $5+\sqrt{5}·\sqrt{5·4}$
= $5+\sqrt{5}·\sqrt{5}·\sqrt{4}$
= $5+5·2$
= $5+10$
= $15$

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

$\left(\sqrt{9}-\sqrt{5}\right)·\left(\sqrt{9}+\sqrt{5}\right)$ = ${\left(\sqrt{9}\right)}^2-{\left(\sqrt{5}\right)}^2$
= $9-5$
= $4$

$\frac{\sqrt{12x}}{\sqrt{3x}}$
= $\frac{\sqrt{12}·\sqrt{x}}{\sqrt{3}·\sqrt{x}}$
= $\frac{\sqrt{12}}{\sqrt{3}}$
= $\sqrt{\frac{12}{3}}$
= $\sqrt{4}$
= $2$

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

$\sqrt{22}+2\sqrt{22}$
= $3\sqrt{22}$