Write $\sqrt{-38}$ as an imaginary number involving $i$.
Do not use a decimal approximation for square roots. For example to enter a number like $5 i \sqrt{7}$, type 5 isqrt7. Preview your answer before submitting!
\[
\sqrt{-38}=
\]
Final Answer: \(\boxed{6.164414002968976i}\)
Step 1 :The square root of a negative number can be written as an imaginary number. The square root of -1 is represented by the imaginary unit 'i'.
Step 2 :So, the square root of -38 can be written as the square root of 38 times the square root of -1, which is 'i'.
Step 3 :Therefore, the square root of -38 is equal to the square root of 38 times 'i'.
Step 4 :\(\sqrt{-38} = \sqrt{38} \times i\)
Step 5 :Calculate the square root of 38 to get approximately 6.164414002968976.
Step 6 :Therefore, \(\sqrt{-38} = 6.164414002968976i\)
Step 7 :Final Answer: \(\boxed{6.164414002968976i}\)