To evaluate the expression \(\sqrt{19} - \frac{3}{2}\), we first find the square root of 19.
\(\sqrt{19} \approx 4.3589\).
Then we subtract \(\frac{3}{2}\), which is equal to \(1.5\):
\[ \sqrt{19} - \frac{3}{2} \approx 4.3589 - 1.5 = 2.8589. \]
The result, approximately \(2.8589\), is a positive real number. Thus, the expression \(\sqrt{19} - \frac{3}{2}\) results in a positive real number.