What type of number will result from the expression  19−−√−32 ?(1 point)

Responses

a whole number
a whole number

an irrational number
an irrational number

an integer
an integer

a rational number

1 answer

To evaluate the expression \( \sqrt{19} - 32 \):

  1. \( \sqrt{19} \) is approximately \( 4.36 \) (since \( 4.36^2 \approx 19 \)).
  2. Therefore, \( \sqrt{19} - 32 \) is approximately \( 4.36 - 32 = -27.64 \).

Now, let's classify the result:

  • Whole numbers are non-negative integers (0, 1, 2, ...), and since the result is negative, it cannot be a whole number.
  • Irrational numbers cannot be expressed as a fraction of two integers and since \( \sqrt{19} \) is irrational, \( \sqrt{19} - 32 \) maintains this property, thus it is an irrational number.
  • Integers are whole numbers that can be positive, negative, or zero. The result \( -27.64 \) is not an integer.
  • Rational numbers can be expressed as a fraction of two integers, and since irrational numbers are not rational, \( \sqrt{19} - 32 \) is not a rational number but rather remains irrational.

Thus, the best classification of the expression \( \sqrt{19} - 32 \) is that it results in an irrational number.

So the answer is: an irrational number.