$\frac{\sqrt{108}}{\sqrt{3}}$
= $\sqrt{\frac{108}{3}}$
= $\sqrt{36}$
= 6

$\sqrt{\mathrm{0,003}}·\sqrt{\mathrm{7,5}}$
= $\sqrt{\mathrm{0,003}·\mathrm{7,5}}$
= $\sqrt{\mathrm{0,0225}}$
= 0.15

$\sqrt{2}·\left(\sqrt{2}+\sqrt{50}\right)$
= $\sqrt{2}·\sqrt{2}+\sqrt{2}·\sqrt{50}$
= $2+\sqrt{2}·\sqrt{2·25}$
= $2+\sqrt{2}·\sqrt{2}·\sqrt{25}$
= $2+2·5$
= $2+10$
= $12$

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

${\left(\sqrt{5}-\sqrt{180}\right)}^2$ = ${\left(\sqrt{5}\right)}^2-2·\sqrt{5}·\sqrt{180}+{\left(\sqrt{180}\right)}^2$
= $5-2·\sqrt{5}·\sqrt{5·36}+180$
= $5-2·\sqrt{5}·\sqrt{5}·\sqrt{36}+180$
= $5-2·5·6+180$
= $5-60+180$
= $125$

$\sqrt{16x}-\sqrt{x}$
= $\sqrt{16}·\sqrt{x}-\sqrt{x}$
= $4\sqrt{x}-\sqrt{x}$
= $3\sqrt{x}$

Wir können die $\sqrt{13}$ wie Einheiten behandeln und einfach verrechnen.

$\sqrt{13}-2\sqrt{13}$
= $-\sqrt{13}$