What type of number will result from the expression 19−−√−32

Question

19−3/2
?(1 point)
Responses
an irrational number
an irrational number
an integer
an integer
a rational number
a rational number
a whole number
a whole number

Answer 1

To evaluate the expression \( \sqrt{19} - \frac{3}{2} \), we first note that:

1. \( \sqrt{19} \) is an irrational number because 19 is not a perfect square.
2. \( \frac{3}{2} \) is a rational number.

Now, when you subtract a rational number ( \( \frac{3}{2} \) ) from an irrational number ( \( \sqrt{19} \) ), the result will always be irrational. This is because the set of rational numbers does not contain any irrational numbers, and subtracting a rational number from an irrational number cannot "cancel out" the irrationality.

Therefore, the result of the expression \( \sqrt{19} - \frac{3}{2} \) will be an irrational number.