Answer
$10a^3b^3\sqrt{2b}$
Work Step by Step
Recall the property (pg. 367):
$\sqrt[n]{a}\cdot \sqrt[n]{b}=\sqrt[n]{ab}$ (if $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers)
Applying this property, the given expression simplifies to:
$=\sqrt{2\cdot 100a^6b^6b}$
$=\sqrt{100a^6b^6 \cdot 2b}$
$=\sqrt{100}\cdot \sqrt{a^6b^6} \cdot \sqrt{2b}$
$=\sqrt{10^2} \cdot \sqrt{(a^3)^2(b^3)^2} \cdot \sqrt{2b}$
$=10a^3b^3\sqrt{2b}$
