Hello,
A rational number is any number that can be expressed as a fraction (using integers).
For answer choice A, [tex] \sqrt{6} + 0.5 [/tex] is ≈ 2.949, which cannot be expressed as a fraction.
For answer choice B, Pi is not a rational number, and the sum of any number and pi cannot be rational.
For answer choice C, -3.5 is a rational number, which can be represented by -7/2. When 0.5, or 1/2, is added, we get -3, which can be represented by -6/2.
So, the answer is C, but we should check answer D just to make sure it does not work.
0.5050050005... is not a rational number that can be represented by a fraction. It is infinite, and when added to 0.5 is 1.050050005, which cannot be represented by a fraction and is therefore not rational.
The answer is C.
Hope this helps!
