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

$\sqrt{\mathrm{1,2}}·\sqrt{\mathrm{0,003}}$
= $\sqrt{\mathrm{1,2}·\mathrm{0,003}}$
= $\sqrt{\mathrm{0,0036}}$
= 0.06

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

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

$\left(\sqrt{8}-\sqrt{3}\right)·\left(\sqrt{8}+\sqrt{3}\right)$ = ${\left(\sqrt{8}\right)}^2-{\left(\sqrt{3}\right)}^2$
= $8-3$
= $5$

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

Wir können die $\sqrt{32}$ wie Einheiten behandeln und einfach verrechnen.

$\sqrt{32}-\sqrt{32}$
= 0