Let's break down the expression step-by-step to determine the type of number resulting from [tex]\(\sqrt{19} - \frac{3}{2}\)[/tex].
1. Calculate [tex]\(\sqrt{19}\)[/tex]:
- The square root of 19 ([tex]\(\sqrt{19}\)[/tex]) is approximately 4.358898943540674.
2. Calculate [tex]\(\frac{3}{2}\)[/tex]:
- The fraction [tex]\(\frac{3}{2}\)[/tex] is equal to 1.5.
3. Subtract [tex]\(\frac{3}{2}\)[/tex] from [tex]\(\sqrt{19}\)[/tex]:
- We now perform the subtraction: [tex]\(4.358898943540674 - 1.5\)[/tex].
- The result of this subtraction is approximately 2.858898943540674.
4. Determine the type of number:
- The result, 2.858898943540674, is not a whole number or an integer because it has a fractional part.
- To determine if it is rational or irrational, we need to see if it can be expressed as a fraction.
In this case, 2.858898943540674 is a rational number because it is derived from operations on rational and irrational numbers but the result itself has a terminating decimal, suggesting it can be represented as a fraction.
So, the type of number resulting from the expression [tex]\(\sqrt{19} - \frac{3}{2}\)[/tex] is:
- a rational number.
