Answer
$-\sqrt{14}$
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:
$=\sqrt{7(-1)} \cdot \sqrt{2(-1)}
\\=(\sqrt{7} \cdot \sqrt{-1}) \cdot (\sqrt{2} \cdot \sqrt{-1})
\\=(\sqrt{7} \cdot i)(\sqrt{2} \cdot i)
\\=i^2\sqrt{7} \cdot \sqrt{2}
\\=i^2\sqrt{7\cdot 2}
\\=i^2\sqrt{14}$
Use rule (2) above to obtain:
$=(-1)\sqrt{14}
\\=-\sqrt{14}$
