## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$a^{5}b^{5}\sqrt{b}$
Extracting the factors that are perfect roots of the given index, the given expression, $\sqrt{a^{10}b^{11}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{a^{10}b^{10}\cdot b} \\\\= \sqrt{(a^{5}b^{5})^2\cdot b} \\\\= a^{5}b^{5}\sqrt{b} \end{array} * Note that it is assumed that no radicands were formed by raising negative numbers to even powers.