Prove that \(4+\sqrt{97}\) is irrational.
Proof:
Let \(4+\sqrt{97}\) is .
Therefore, \(4+\sqrt{97}\) can be expressed as \(\frac{p}{q}\), where \(p\) and \(q\) are any two integers such that \(q\neq 0\)
\(4+\sqrt{97}=\frac{p}{q}\)
Hence, \(\sqrt{97}=\frac{p}{q}-\)
\(\frac{p}{q}-4\) is as \(p\) and \(q\) are .
Therefore, \(\sqrt{97}\) is which contradicts the fact that \(\sqrt{97}\) is .
Hence, \(4+\sqrt{97}\) is .