To determine whether the number \( 4 + \pi \) is rational or irrational, we need to analyze the components of the expression.
A rational number is defined as a number that can be expressed as the quotient of two integers (i.e., in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \)). An irrational number, on the other hand, cannot be expressed in this way.
The number \( 4 \) is a rational number because it can be represented as \( \frac{4}{1} \). The number \( \pi \), however, is known to be irrational.
The sum of a rational number and an irrational number is always irrational. Therefore, since \( 4 \) is rational and \( \pi \) is irrational, the sum \( 4 + \pi \) must also be irrational.
In conclusion, \( 4 + \pi \) is an irrational number.