Answer
$i\sqrt{20}$;
$i\sqrt{4\cdot5}$;
$2i\sqrt{5}$
Work Step by Step
RECALL:
(1) $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$
(2) $\sqrt{-1} = i$
Use rule (1) above to obtain:
$\sqrt{-20}
\\= \sqrt{(-1)(20)}
\\= \sqrt{-1} \cdot \sqrt{20}$
Use rule (2) above to obtain:
$=i\sqrt{20}$
Use rule (1) again to obtain:
$=i\sqrt{4\cdot5}
\\=i\sqrt{4} \sqrt{5}
\\=i\cdot 2 \sqrt{5}
\\=2i\sqrt{5}$
Therefore, the missing expressions in the given statement, in order, are:
$i\sqrt{20}$;
$i\sqrt{4\cdot5}$;
$2i\sqrt{5}$
