Answer
$-5\sqrt{7}$
Work Step by Step
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:
$=5(-1)\sqrt{7}
\\=-5\sqrt{7}$
