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) Rational Irrational xz x+y xy y+z

Question

which answers are rational or irrational? answer correctly

Answer 1

Let's analyze each expression to determine if its value is rational or irrational:

1. \( xz \): Since \( x \) is a non-zero rational number and \( z \) is an irrational number, the product of a rational number and an irrational number is always irrational.

   • Answer: Irrational

2. \( x + y \): Both \( x \) and \( y \) are non-zero rational numbers. The sum of two rational numbers is rational.

   • Answer: Rational

3. \( xy \): Again, both \( x \) and \( y \) are non-zero rational numbers. The product of two rational numbers is rational.

   • Answer: Rational

4. \( y + z \): 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.

   • Answer: Irrational

In summary:

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