\(1)
\\ \sqrt{100a^3}=\sqrt{10^2\cdot a^2\cdot a}=\sqrt{10^2}\cdot\sqrt {a^2}\cdot\sqrt {a}=10\cdot a\cdot \sqrt a=10a\sqrt a\\\\ \\ 2)\\ \sqrt[3]{8a^3b^5}=\sqrt[3]{2^3\cdot a^3\cdot b^3\cdot b^2}=\sqrt[3]{2^3}\cdot\sqrt[3]{a^3}\cdot\sqrt[3]{b^3}\cdot\sqrt[3]{b^2}=2\cdot a\cdot b\cdot\sqrt[3]{b^2}=\\\\ ~\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad =2ab(\sqrt[3]{b^2})\)
