## Intermediate Algebra for College Students (7th Edition)

$-5\sqrt{7}$
RECALL: (1) $\sqrt{-1}=i$ (2) $i^2=-1$ (3) $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$ Simplify each radical by using rules (1) and (3) above: $=\sqrt{7(-1)} \cdot \sqrt{25(-1)} \\=(\sqrt{7} \cdot \sqrt{-1}) \cdot \sqrt{5^2(-1)} \\=(\sqrt{7} \cdot i) \cdot 5\sqrt{-1} \\=i\sqrt{7} \cdot 5i \\=5i^2\sqrt{7}$ Use rule (2) above to obtain: $=5(-1)\sqrt{7} \\=-5\sqrt{7}$