$\frac{\sqrt{32}}{\sqrt{2}}$
= $\sqrt{\frac{32}{2}}$
= $\sqrt{16}$
= 4

$\frac{\sqrt{\frac{1}{4}}}{\sqrt{1}}$
= $\sqrt{\frac{\frac{1}{4}}{1}}$
= $\sqrt{\frac{1}{4}·1}$
= $\sqrt{\frac{1}{4}}$
= $\frac{1}{2}$

$\left(\sqrt{125}+\sqrt{5}\right)·\sqrt{5}$
= $\sqrt{125}·\sqrt{5}+\sqrt{5}·\sqrt{5}$
= $\sqrt{5·25}·\sqrt{5}+5$
= $\sqrt{25}·\sqrt{5}·\sqrt{5}+5$
= $5·5+5$
= $25+5$
= $30$

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

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

$\frac{\sqrt{12x}}{\sqrt{3x}}$
= $\frac{\sqrt{12}·\sqrt{x}}{\sqrt{3}·\sqrt{x}}$
= $\frac{\sqrt{12}}{\sqrt{3}}$
= $\sqrt{\frac{12}{3}}$
= $\sqrt{4}$
= $2$

Wir können die $\sqrt{20}$ wie Einheiten behandeln und einfach verrechnen.

$-3\sqrt{20}-7\sqrt{20}$
= $-10\sqrt{20}$