Question

Which statement is true about all irrational numbers? They can be written as a ________.
Repeating decimal without end
Fraction
Decimal that ends
Non-repeating decimal without end

Answer 1

Let 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)
xy
y+z
xz
x+y

Answer 2

The true statement about all irrational numbers is: They can be written as a **non-repeating decimal without end**.

Irrational numbers cannot be expressed as a fraction of two integers, and their decimal representation goes on forever without repeating.

Answer 3

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

1. **Expression: \(xy\)**
- **Value:** Rational
- **Reason:** The product of two rational numbers is rational.

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

3. **Expression: \(xz\)**
- **Value:** Irrational
- **Reason:** The product of a rational number (non-zero) and an irrational number is irrational.

4. **Expression: \(x + y\)**
- **Value:** Rational
- **Reason:** The sum of two rational numbers is rational.

### Summary Table
| Expression | Value |
|------------|-------------|
| \(xy\) | Rational |
| \(y + z\) | Irrational |
| \(xz\) | Irrational |
| \(x + y\) | Rational |