To evaluate the expression \( \sqrt{19} - \frac{3}{2} \), we need to consider the nature of \( \sqrt{19} \) and \( \frac{3}{2} \).
-
Determine \( \sqrt{19} \):
- The square root of 19 is approximately 4.3589, which is an irrational number since 19 is not a perfect square.
-
Rationality of \( \frac{3}{2} \):
- The fraction \( \frac{3}{2} \) is a rational number.
-
Combining the two:
- When you subtract a rational number from an irrational number, the result is always an irrational number.
So, \( \sqrt{19} - \frac{3}{2} \) will be an irrational number.
Thus, the correct response is:
B) an irrational number