To determine if the number \(\sqrt{42} + 6\) is rational or irrational, we first consider the nature of \(\sqrt{42}\).
The square root of 42, \(\sqrt{42}\), is an irrational number because 42 is not a perfect square (it cannot be expressed as the square of a whole number).
Now, let's look at \(\sqrt{42} + 6\). Here, 6 is a rational number (since it can be expressed as \(6/1\)). The sum of an irrational number and a rational number is always irrational.
Therefore, \(\sqrt{42} + 6\) is an irrational number.