$\frac{\sqrt{18}}{\sqrt{2}}$
= $\sqrt{\frac{18}{2}}$
= $\sqrt{9}$
= 3

$\sqrt{20}·\sqrt{\mathrm{0,008}}$
= $\sqrt{20·\mathrm{0,008}}$
= $\sqrt{\mathrm{0,16}}$
= 0.4

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

Nach der 1. binomischen Formel ((a+b)²=a²+2ab+b²) gilt:

${\left(\sqrt{2}+\sqrt{72}\right)}^2$ = ${\left(\sqrt{2}\right)}^2+2·\sqrt{2}·\sqrt{72}+{\left(\sqrt{72}\right)}^2$
= $2+2·\sqrt{2}·\sqrt{2·36}+72$
= $2+2·\sqrt{2}·\sqrt{2}·\sqrt{36}+72$
= $2+2·2·6+72$
= $2+24+72$
= $98$

$\frac{\sqrt{160x}}{\sqrt{10x}}$
= $\frac{\sqrt{160}·\sqrt{x}}{\sqrt{10}·\sqrt{x}}$
= $\frac{\sqrt{160}}{\sqrt{10}}$
= $\sqrt{\frac{160}{10}}$
= $\sqrt{16}$
= $4$

Wir können die $\sqrt{39}$ wie Einheiten behandeln und einfach verrechnen.

$-12\sqrt{39}-8\sqrt{39}$
= $-20\sqrt{39}$