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

$\sqrt{\frac{1}{72}}·\sqrt{2}$
= $\sqrt{\frac{1}{72}·2}$
= $\sqrt{\frac{1}{36}·1}$
= $\sqrt{\frac{1}{36}}$
= $\frac{1}{6}$

$\left(\sqrt{3}+\sqrt{108}\right)·\sqrt{3}$
= $\sqrt{3}·\sqrt{3}+\sqrt{108}·\sqrt{3}$
= $3+\sqrt{3·36}·\sqrt{3}$
= $3+\sqrt{36}·\sqrt{3}·\sqrt{3}$
= $3+6·3$
= $3+18$
= $21$

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

$\left(\sqrt{5}-4\right)·\left(\sqrt{5}+4\right)$ = ${\left(\sqrt{5}\right)}^2-4^2$
= $5-16$
= $-11$

$\sqrt{3x}·\sqrt{108x}$
= $\sqrt{3}·\sqrt{x}·\sqrt{108}·\sqrt{x}$
= $\sqrt{3}·\sqrt{108}·\sqrt{x}·\sqrt{x}$
= $\sqrt{3}·\sqrt{3·36}·x$
= $\sqrt{3}·\sqrt{3}·\sqrt{36}·x$
= $3·6·x$
= $18x$

Wir können die $\sqrt{46}$ wie Einheiten behandeln und einfach die $\sqrt{46}$ verrechnen.

$-17\sqrt{46}-8\sqrt{46}$
= $-25\sqrt{46}$