Question

et x and y be non-zero, rational numbers, and let z be an irrational number. In
the first column of the table below is an expression. In the second column,
determine whether the value of each expression is rational or irrational.
(4 points)
x + y
xz
Y+z
xy
Rational
Irrational

Answer 1

Let's analyze each expression to determine whether its value is rational or irrational when \(x\) and \(y\) are non-zero rational numbers, and \(z\) is an irrational number.

1. **Expression:** \(x + y\)
- **Value:** \(x + y\) is the sum of two rational numbers.
- **Type:** Rational

2. **Expression:** \(xz\)
- **Value:** The product of a rational number (\(x\)) and an irrational number (\(z\)).
- **Type:** Irrational

3. **Expression:** \(y + z\)
- **Value:** The sum of a rational number (\(y\)) and an irrational number (\(z\)).
- **Type:** Irrational

4. **Expression:** \(xy\)
- **Value:** The product of two rational numbers (\(x\) and \(y\)).
- **Type:** Rational

Here’s the summary in the requested format:

| Expression | Value Type |
|------------|------------|
| \(x + y\) | Rational |
| \(xz\) | Irrational |
| \(y + z\) | Irrational |
| \(xy\) | Rational |