Show that \(3\sqrt{2}\) is irrational.
Proof:
Let \(3\sqrt{2}\) is .
By definition, \(3\sqrt{2}\)
That is, \(3\sqrt{2}=\) be number, where \(p\) and \(q\) are and \(q\neq 0\)
On simplification we get, \(\sqrt{2}=\frac{\frac{p}{q}}{3}\)
Since, \(p\) and \(q\) are integers, \(\frac{\frac{p}{q}}{3}\) will also be .
Therefore, \(\sqrt{2}\) is .
This the fact that \(\sqrt{2}\) is .
Hence, \(3\sqrt{2}\) is .