The given expression can be rewritten as
[tex]\sqrt[]{-169}=\sqrt[]{-1\times13\times13}[/tex]
which is equivalent to
[tex]\sqrt[]{-169}=\sqrt[]{-1}\times\sqrt[]{13^2}[/tex]
By the definition of imaginary number
[tex]\sqrt[]{-1}=i[/tex]
and
[tex]\sqrt[]{13^2}=13[/tex]
the answer is:
[tex]\sqrt[]{-169}=13i[/tex]
which corresponds to option C
