$\sqrt{360}·\sqrt{10}$
= $\sqrt{10·36}·\sqrt{10}$
= $\sqrt{36}·\sqrt{10}·\sqrt{10}$
= $6·10$
= $60$

$\frac{\sqrt{\mathrm{2,5}}}{\sqrt{\mathrm{0,1}}}$
= $\sqrt{\frac{2.5}{0.1}}$
= $\sqrt{25}$
= $\sqrt{25}$
= 5

$\sqrt{3}·\left(\sqrt{75}+\sqrt{3}\right)$
= $\sqrt{3}·\sqrt{75}+\sqrt{3}·\sqrt{3}$
= $\sqrt{3}·\sqrt{3·25}+3$
= $\sqrt{3}·\sqrt{3}·\sqrt{25}+3$
= $3·5+3$
= $15+3$
= $18$

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

${\left(\sqrt{3}-\sqrt{108}\right)}^2$ = ${\left(\sqrt{3}\right)}^2-2·\sqrt{3}·\sqrt{108}+{\left(\sqrt{108}\right)}^2$
= $3-2·\sqrt{3}·\sqrt{3·36}+108$
= $3-2·\sqrt{3}·\sqrt{3}·\sqrt{36}+108$
= $3-2·3·6+108$
= $3-36+108$
= $75$

$\sqrt{x}+\sqrt{4x}$
= $\sqrt{x}+\sqrt{4}·\sqrt{x}$
= $\sqrt{x}+2\sqrt{x}$
= $3\sqrt{x}$

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

${\left(\sqrt{32}+\sqrt{2}\right)}^2$ = ${\left(\sqrt{32}\right)}^2+2·\sqrt{32}·\sqrt{2}+{\left(\sqrt{2}\right)}^2$
= $32+2·\sqrt{2·16}·\sqrt{2}+2$
= $32+2·\sqrt{16}·\sqrt{2}·\sqrt{2}+2$
= $32+2·4·2+2$
= $32+16+2$
= $50$