Answer
$-2b^{3}\sqrt (5a)$
Work Step by Step
$-\sqrt (20ab^{6})=-\sqrt (4\times 5a\times b^{6})=-(\sqrt 4\times \sqrt (5a)\times \sqrt (b^{6}))=-(2b^{3}\sqrt (5a))=-2b^{3}\sqrt (5a)$
We know that $\sqrt 4=2$, because $2^{2}=4$. We also know that $\sqrt (b^{6})=b^{3}$, because $(b^{3})^{2}=b^{3\times2}=b^{6}$
