$\frac{\sqrt{72}}{\sqrt{2}}$
= $\sqrt{\frac{72}{2}}$
= $\sqrt{36}$
= 6

$\frac{\sqrt{\mathrm{0,02}}}{\sqrt{\mathrm{0,5}}}$
= $\sqrt{\frac{0.02}{0.5}}$
= $\sqrt{\frac{0.2}{5}}$
= $\sqrt{\mathrm{0,04}}$
= 0.2

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

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

${\left(\sqrt{3}+\sqrt{48}\right)}^2$ = ${\left(\sqrt{3}\right)}^2+2·\sqrt{3}·\sqrt{48}+{\left(\sqrt{48}\right)}^2$
= $3+2·\sqrt{3}·\sqrt{3·16}+48$
= $3+2·\sqrt{3}·\sqrt{3}·\sqrt{16}+48$
= $3+2·3·4+48$
= $3+24+48$
= $75$

$\sqrt{x}+\sqrt{25x}$
= $\sqrt{x}+\sqrt{25}·\sqrt{x}$
= $\sqrt{x}+5\sqrt{x}$
= $6\sqrt{x}$

Wir können die $\sqrt{33}$ wie Einheiten behandeln und einfach verrechnen.

$-9\sqrt{33}-7\sqrt{33}$
= $-16\sqrt{33}$