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

$\frac{\sqrt{50}}{\sqrt{\mathrm{0,02}}}$
= $\sqrt{\frac{50}{0.02}}$
= $\sqrt{\frac{5000}{2}}$
= $\sqrt{2500}$
= 50

$\sqrt{10}·\left(\sqrt{10}+\sqrt{360}\right)$
= $\sqrt{10}·\sqrt{10}+\sqrt{10}·\sqrt{360}$
= $10+\sqrt{10}·\sqrt{10·36}$
= $10+\sqrt{10}·\sqrt{10}·\sqrt{36}$
= $10+10·6$
= $10+60$
= $70$

Nach der 3. binomischen Formel ((a+b)(a-b)=a²-b²) gilt:

$\left(\sqrt{9}-6\right)·\left(\sqrt{9}+6\right)$ = ${\left(\sqrt{9}\right)}^2-6^2$
= $9-36$
= $-27$

$\sqrt{9x}-4\sqrt{x}$
= $\sqrt{9}·\sqrt{x}-4\sqrt{x}$
= $3\sqrt{x}-4\sqrt{x}$
= $-\sqrt{x}$

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

$-3\sqrt{24}-5\sqrt{24}$
= $-8\sqrt{24}$