Is the number 6 + 𝜋 rational or irrational?

Answer 1

To determine whether the number \( 6 + \pi \) is rational or irrational, we need to consider the properties of the numbers involved.

1. The number 6 is a rational number because it can be expressed as the fraction \( \frac{6}{1} \).
2. The number \( \pi \) is known to be an irrational number. This means that it cannot be expressed as a fraction \( \frac{a}{b} \) where \( a \) and \( b \) are integers.

The sum of a rational number and an irrational number is always irrational. Therefore, since \( 6 \) is rational and \( \pi \) is irrational, their sum \( 6 + \pi \) must also be irrational.

In conclusion, \( 6 + \pi \) is irrational.