To determine which expression represents a rational number given that \( p \) and \( q \) are rational numbers and \( r \) is an irrational number, let's analyze each option.
A. \( p + r \)
- Here, \( p \) is rational and \( r \) is irrational. The sum of a rational number and an irrational number is always irrational.
- Thus, this expression is not rational.
B. \( p + pr \)
- The term \( pr \) (where \( p \) is rational and \( r \) is irrational) is irrational since the product of a nonzero rational number and an irrational number is irrational. Therefore, \( p + pr \) (rational + irrational) is also irrational.
- Thus, this expression is not rational.
C. \( p + q \)
- Both \( p \) and \( q \) are rational numbers. The sum of two rational numbers is rational.
- Thus, this expression is rational.
D. \( p + qr \)
- Here, \( qr \) (where \( q \) is rational and \( r \) is irrational) is irrational. Therefore, \( p + qr \) (rational + irrational) is also irrational.
- Thus, this expression is not rational.
The only expression that represents a rational number is:
C. \( p + q \)
1 answer