Let x and y be non-zero, rational numbers, and z an irrational number in the first of the table below is an expression. In the second column, determine whether expression is rational or irrational(4 points) Rational Irrational x + y; y + z

Answer 1

In the table provided, we can determine the nature of each expression based on the properties of rational and irrational numbers.

1. \(x + y\):

   • Since both \(x\) and \(y\) are non-zero rational numbers, the sum of two rational numbers is also a rational number.
   • Result: Rational

2. \(y + z\):

   • Here, \(y\) is a non-zero rational number and \(z\) is an irrational number. The sum of a rational number and an irrational number is always irrational.
   • Result: Irrational

In summary:

• \(x + y\): Rational
• \(y + z\): Irrational