Suppose that p & q are nonzero rational numbers and z is an irrational number. Which of the following would be rational? Select TWO answers.

Question

the sum of q and z
the product of p and q
the product of p and z
the sum of p and q
the difference of p and z

Answer 1

To determine which of the options will result in a rational number, we will analyze each one:

1. The sum of q and z (q + z): Since \( q \) is rational and \( z \) is irrational, their sum will be irrational. Thus, this is not rational.

2. The product of p and q (p * q): Since both \( p \) and \( q \) are nonzero rational numbers, their product will also be a rational number. Thus, this is rational.

3. The product of p and z (p * z): Here, \( p \) is rational and \( z \) is irrational. The product of a rational number and an irrational number is irrational. Thus, this is not rational.

4. The sum of p and q (p + q): Since both \( p \) and \( q \) are rational, their sum will also be a rational number. Thus, this is rational.

5. The difference of p and z (p - z): Similar to the product case, since \( p \) is rational and \( z \) is irrational, their difference will be irrational. Thus, this is not rational.

After evaluating all options, the two answers that are rational are:

• The product of p and q (p * q)
• The sum of p and q (p + q)