Answer
$-\sqrt{21}$
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:
$=\sqrt{7(-1)} \cdot \sqrt{3(-1)}
\\=(\sqrt{7} \cdot \sqrt{-1}) \cdot (\sqrt{3} \cdot \sqrt{-1})
\\=(\sqrt{7} \cdot i)(\sqrt{3} \cdot i)
\\=i^2\sqrt{7} \cdot \sqrt{3}
\\=i^2\sqrt{7\cdot 3}
\\=i^2\sqrt{21}$
Use rule (2) above to obtain:
$=(-1)\sqrt{21}
\\=-\sqrt{21}$
