Answer
$3i\sqrt{7}$
Work Step by Step
Factor the radicand so that one factor $-1$ to obtain:
$=\sqrt{63(-1)}
\\=\sqrt{9(7)(-1)}
\\=\sqrt{3^2(7)(-1)}$
RECALL:
(1) $\sqrt{abc} = \sqrt{a} \cdot \sqrt{b} \cdot \sqrt{c}$
(2) $\sqrt{-1} = i$
Use rule (1) above to obtain:
$=\sqrt{3^2} \cdot \sqrt{7} \cdot \sqrt{-1}
\\=3 \cdot \sqrt{7} \cdot \sqrt{-1}
\\=3\sqrt{7} \cdot \sqrt{-1}$
Use rule (2) above to obtain:
$=3\sqrt{7} \cdot i
\\=3i\sqrt{7}$
