Answer
$5i\sqrt{5}$
Work Step by Step
Factor the radicand so that one factor $-1$ to obtain:
$=\sqrt{125(-1)}
\\=\sqrt{25(5)(-1)}
\\=\sqrt{5^2(5)(-1)}$
RECALL:
(1) $\sqrt{abc} = \sqrt{a} \cdot \sqrt{b} \cdot \sqrt{c}$
(2) $\sqrt{-1} = i$
Use rule (1) above to obtain:
$=\sqrt{5^2} \cdot \sqrt{5} \cdot \sqrt{-1}
\\=5 \cdot \sqrt{5} \cdot \sqrt{-1}
\\=5\sqrt{5} \cdot \sqrt{-1}$
Use rule (2) above to obtain:
$=5\sqrt{5} \cdot i
\\=5i\sqrt{5}$
