What type of number will result from the expression √19 − 3/2 ?(1 point)

Question

Responses

A) a rational number

B) an irrational number

C) a whole number

D) an integer

Answer 1

To evaluate the expression \( \sqrt{19} - \frac{3}{2} \), we need to consider the nature of \( \sqrt{19} \) and \( \frac{3}{2} \).

1. Determine \( \sqrt{19} \):

   • The square root of 19 is approximately 4.3589, which is an irrational number since 19 is not a perfect square.

2. Rationality of \( \frac{3}{2} \):

   • The fraction \( \frac{3}{2} \) is a rational number.

3. 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