$\text{a)}\sqrt{3600}=\sqrt{36}\cdot \sqrt{100}=6\cdot 10=60$

$\text{b)}\sqrt{1440000}=\sqrt{144}\cdot \sqrt{10000}=12\cdot 100=1200$

$\text{c)}\sqrt[3]{64000}=\sqrt[3]{64}\cdot \sqrt[3]{1000}=4\cdot 10=40$

$\text{d)}\sqrt[3]{-8000}=\sqrt[3]{-8}\cdot \sqrt[3]{1000}=\left(-2\right)\cdot 10=-20$

$\text{e)}\sqrt[3]{-27000000}=\sqrt[3]{-27}\cdot \sqrt[3]{1000000}=\left(-3\right)\cdot 100=-300$

$\text{f)}\sqrt{64000000}=\sqrt{64}\cdot \sqrt{1000000}=8\cdot 1000=8000$