The number represented by x may be rational or irrational
Step-by-step explanation:
Rational and irrational numbers
For this answer, we must remind that a rational number is such that it can be expressed as a fraction. Irrational numbers cannot. Examples of rational numbers are
![-2,\frac{3}{4},0,3.21,1.3333...](/tpl/images/0403/6292/b44bd.png)
Examples of irrational numbers are
![\sqrt{2},\pi, 1+\sqrt{3}, e^5,sin1](/tpl/images/0403/6292/97d26.png)
To help us to better explain this answer, let's suppose
![x=1+\sqrt{2}\ ,\ y=1-\sqrt{2}](/tpl/images/0403/6292/7f464.png)
They both are irrational and their sum is rational as shown:
![x+y=1+\sqrt{2}+1-\sqrt{2}=2](/tpl/images/0403/6292/7fb74.png)
The first option: "The number represented by y must be rational" is false because y is not rational
The second option: "The number represented by X must be rational." and the last option: "The number represented by x must be rational and the number
represented by y must be rational" are equally false.
The only true option is: "The number represented by x may be rational or irrational".
We can clearly see one member of a sum doesn't necessarily define it as irrational