$\frac{\sqrt{360}}{\sqrt{10}}$
= $\sqrt{\frac{360}{10}}$
= $\sqrt{36}$
= 6

$\frac{\sqrt{8000}}{\sqrt{\mathrm{0,05}}}$
= $\sqrt{\frac{8000}{0.05}}$
= $\sqrt{\frac{800.000}{5}}$
= $\sqrt{160000}$
= 400

$\sqrt{2}·\left(\sqrt{8}+\sqrt{2}\right)$
= $\sqrt{2}·\sqrt{8}+\sqrt{2}·\sqrt{2}$
= $\sqrt{2}·\sqrt{2·4}+2$
= $\sqrt{2}·\sqrt{2}·\sqrt{4}+2$
= $2·2+2$
= $4+2$
= $6$

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

${\left(\sqrt{10}+\sqrt{40}\right)}^2$ = ${\left(\sqrt{10}\right)}^2+2·\sqrt{10}·\sqrt{40}+{\left(\sqrt{40}\right)}^2$
= $10+2·\sqrt{10}·\sqrt{10·4}+40$
= $10+2·\sqrt{10}·\sqrt{10}·\sqrt{4}+40$
= $10+2·10·2+40$
= $10+40+40$
= $90$

$\frac{\sqrt{75x}}{\sqrt{3x}}$
= $\frac{\sqrt{75}·\sqrt{x}}{\sqrt{3}·\sqrt{x}}$
= $\frac{\sqrt{75}}{\sqrt{3}}$
= $\sqrt{\frac{75}{3}}$
= $\sqrt{25}$
= $5$

Wir können die $\sqrt{11}$ wie Einheiten behandeln und einfach die $\sqrt{11}$ verrechnen.

$5\sqrt{11}+7\sqrt{11}$
= $12\sqrt{11}$