To simplify the number we use the following rules:
a) [tex] \sqrt{-1}=i [/tex]
b) [tex] \sqrt{a*b}= \sqrt{a} * \sqrt{b} [/tex]
using these rules:
[tex]\sqrt{-38}= \sqrt{38*(-1)}= \sqrt{38}* \sqrt{-1} =\sqrt{38}* i=\sqrt{38}i[/tex]
square root of 38 cannot be simplified any further, since 38 has no perfect square factors.
Answer: \sqrt{38}i
