The square root of 78 is irrational.
To determine whether a number is rational or irrational, we can consider its prime factorization. The prime factors of 78 are \(2 \times 3 \times 13\). Since 78 is not a perfect square (it cannot be expressed as \(n^2\) for some integer \(n\)), its square root cannot be expressed as a fraction of two integers.
Therefore, \(\sqrt{78}\) is irrational.