$\frac{\sqrt{180}}{\sqrt{5}}$
= $\sqrt{\frac{180}{5}}$
= $\sqrt{36}$
= 6

$\frac{\sqrt{3600}}{\sqrt{\mathrm{0,01}}}$
= $\sqrt{\frac{3600}{0.01}}$
= $\sqrt{360000}$
= $\sqrt{360000}$
= 600

$\left(\sqrt{5}+\sqrt{180}\right)·\sqrt{5}$
= $\sqrt{5}·\sqrt{5}+\sqrt{180}·\sqrt{5}$
= $5+\sqrt{5·36}·\sqrt{5}$
= $5+\sqrt{36}·\sqrt{5}·\sqrt{5}$
= $5+6·5$
= $5+30$
= $35$

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

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

$\sqrt{36x}+2\sqrt{x}$
= $\sqrt{36}·\sqrt{x}+2\sqrt{x}$
= $6\sqrt{x}+2\sqrt{x}$
= $8\sqrt{x}$

Wir können die $\sqrt{24}$ wie Einheiten behandeln und einfach verrechnen.

$-7\sqrt{24}-9\sqrt{24}$
= $-16\sqrt{24}$