Answer:
[tex]\sqrt{-5}=i\sqrt{5}[/tex]
[tex]\sqrt{-25}=5i[/tex]
Step-by-step explanation:
i is an imaginary unit, this means
[tex]i^2=-1[/tex]
Rewrite -5 as [tex]5\cdot (-1)=5\cdot i^2,[/tex]
then
[tex]\sqrt{-5}=\sqrt{5i^2}=\sqrt{5}\cdot \sqrt{i^2}=\sqrt{5}\cdot i=i\sqrt{5}[/tex]
Rewrite -25 as [tex]-25=25\cdot (-1)=25\cdot i^2,[/tex]
then
[tex]\sqrt{-25}=\sqrt{25\cdot i^2}=\sqrt{25}\cdot \sqrt{i^2}=5\cdot i=5i[/tex]
