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

$5i\sqrt{2}$
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the given expression is equivalent to\begin{array}{l}\require{cancel} \sqrt{-50} \\\\= \sqrt{-1}\cdot\sqrt{50} .\end{array} Using $i=\sqrt{-1}$ and extracting the factors that are perfect powers of the index, the expression above simplifies to \begin{array}{l}\require{cancel} \sqrt{-1}\cdot\sqrt{50} \\\\= i\sqrt{25\cdot2} \\\\= i\sqrt{(5)^2\cdot2} \\\\= 5i\sqrt{2} .\end{array}