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

$\sqrt{80}·\sqrt{\mathrm{0,002}}$
= $\sqrt{80·\mathrm{0,002}}$
= $\sqrt{\mathrm{0,16}}$
= 0.4

$\sqrt{10}·\left(\sqrt{40}+\sqrt{10}\right)$
= $\sqrt{10}·\sqrt{40}+\sqrt{10}·\sqrt{10}$
= $\sqrt{10}·\sqrt{10·4}+10$
= $\sqrt{10}·\sqrt{10}·\sqrt{4}+10$
= $10·2+10$
= $20+10$
= $30$

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

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

$2\sqrt{x}+\sqrt{49x}$
= $2\sqrt{x}+\sqrt{49}·\sqrt{x}$
= $2\sqrt{x}+7\sqrt{x}$
= $9\sqrt{x}$

Wir können die $\sqrt{18}$ wie Einheiten behandeln und einfach verrechnen.

$-9\sqrt{18}-5\sqrt{18}$
= $-14\sqrt{18}$