Answer:
The answer would be 10i.
Step-by-step explanation:
Given expression,
[tex]\sqrt{-100}[/tex]
[tex]=\sqrt{-(10)^2}[/tex]
[tex]=\sqrt{-1}\times \sqrt{10^2}[/tex] [tex](\because \sqrt{ab}=\sqrt{a}\times \sqrt{b})[/tex]
[tex]=\sqrt{-1}\times (10^2)^\frac{1}{2}[/tex] [tex](\because \sqrt{a}=a^\frac{1}{2})[/tex]
[tex]=i\times (10)^{2\times \frac{1}{2}}[/tex] [tex](\because (a^m)^n = a^{mn})[/tex]
[tex]=10i[/tex]
