Answer
real part: $\sqrt{3}$
imaginary part: 2
Work Step by Step
If the complex number is $a+bi$, then the real part is $a$ and the imaginary part is $b$. We have $\sqrt{3}+\sqrt{-4}=\sqrt{3}+\sqrt{4}i=\sqrt{3}+2i$, so the real part is $\sqrt{3}$ and the imaginary part is $2$.