Answer
$-2\sqrt{6}$
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:
$=\sqrt{8(-1)} \cdot \sqrt{3(-1)}
\\=(\sqrt{8} \cdot \sqrt{-1}) \cdot (\sqrt{3} \cdot \sqrt{-1})
\\=(\sqrt{8} \cdot i) \cdot (\sqrt{3} \cdot i)
\\=i^2\sqrt{8(3)}
\\=i^2\sqrt{24}
\\=i^2\sqrt{4(6)}
\\=i^2\sqrt{2^2(6)}
\\=i^2\cdot 2\sqrt{6}
\\=2i^2\sqrt{6}$
Use rule (2) above to obtain:
$=2(-1)\sqrt{6}
\\=-2\sqrt{6}$
