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

$\frac{\sqrt{\frac{1}{40}}}{\sqrt{\frac{1}{10}}}$
= $\sqrt{\frac{\frac{1}{40}}{\frac{1}{10}}}$
= $\sqrt{\frac{1}{40}·10}$
= $\sqrt{\frac{1}{4}·1}$
= $\sqrt{\frac{1}{4}}$
= $\frac{1}{2}$

$\sqrt{3}·\left(\sqrt{3}+\sqrt{27}\right)$
= $\sqrt{3}·\sqrt{3}+\sqrt{3}·\sqrt{27}$
= $3+\sqrt{3}·\sqrt{3·9}$
= $3+\sqrt{3}·\sqrt{3}·\sqrt{9}$
= $3+3·3$
= $3+9$
= $12$

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

${\left(\sqrt{2}+\sqrt{50}\right)}^2$ = ${\left(\sqrt{2}\right)}^2+2·\sqrt{2}·\sqrt{50}+{\left(\sqrt{50}\right)}^2$
= $2+2·\sqrt{2}·\sqrt{2·25}+50$
= $2+2·\sqrt{2}·\sqrt{2}·\sqrt{25}+50$
= $2+2·2·5+50$
= $2+20+50$
= $72$

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

Wir können die $\sqrt{26}$ wie Einheiten behandeln und einfach verrechnen.

$14\sqrt{26}+4\sqrt{26}$
= $18\sqrt{26}$